CAPITOLO 1 1

Testo completo

(1)

(2) ! #"%$&'(!)+*-, . /10325476#8:9<;>=@?@A7BC9<;7DC;>6#8:A7;7EFEF67GH;>DI6>A7EJBC07=@BIA7?@DIBK=L?@EF?@9<9<67EFBI8L9MBI=@N76>O#67BP=@EFBI8:9M?@DCDQBKDIBI2747BCO5B 076#GR?@9<BI=@BTSUBI0A7?@EF9<BI=@;#DI?@EJ6VBIDTWXZYZ[\6VDI6V]#EJ?@07O#6#^_^`6V=@N76VDIBTO76#8:=@EFBIa7;#07;V056#DCDI?cb<?@8:6 076#GR?@9<BI=@?@dfe\6#O#EJ67GR;#gfBI07;7DC9<EJ6#gh=@;7GH6iBC079<67EF?@]#BI8j=@;#07;k=@;#0i470i=@?@GRA7;l678:9<6#EF07;#g GH?@]7076#9<BC=@;>;>65DC6#9<9<EJBC=@;7d monpm qsrut5vct@ruwryxTz7{ xpt5|v#}p}pxT}CxC~PxpKxTwK>v#|xpz7xR mu 47?@07O#;8:BRA7?@EFDI?%O#BRb<?@8:BRO#6#DIDI?%GR?@9<6#EFBQ?%8:BRA76#078:?@gRBC0]76#076#EF67gH?@O470#?%076#9<9<? O#BC8:9MBI07^`BC;7076b<EJ?DI?b<?L8:6DQBC2747BIO#?BC8:;#9<EJ;#A7?627456#DCDI?8:;7DCBIO#?K27456#8:9MC47DI9<BIGR? A7EF6#8:6#059<?c470;#EJO#BC076?cDI4507]#;3:#T@gT8:BC?>0767DCDI6VA5;#8:BI^`BC;#05B=@N76076#DQDC6V;7EFBI67079<?@^`BC;#05B O#6#DIDC6-GR;#DI6#=@;#DI6#d479<9M?@a7BC?@g678:BI8:9<;#05;%=@;#GHA5;#8:9<B=@N76%A7;78L8:;70#;%9<EF;a7?@EJ8:BBI0-4707? b<?@8:6>BC079<6#EJGR6#O7BC?@gK=@N7BI?LGR?@9<?hb<?@8:6H#Ru C@`gKBI03=@45Bu hA7EF678:6#079<6>4703;#EJO#BC076>O#Bu9<BIA7; ;#EFBI6#079<?@^`BI;#07?@DC67gGR?+470¡O#BI8:;#EFO#BI076¢A7;78LBI^_BC;707?@DI6#d/:I£P @¤I¤I¤II¥¦ C§5co#Ru IjB SUXZö©[8L;70#;VbU;#EJGH?@9<BTO#?>GR;#DI6#=@;#DI6V?@DIDC4707]7?@9<6#gT8:=LN767GH?@9<BI^`^`?@ª7BCDQB=@;7GH6ª7?@=L=@N76#9<9<6 ;#EFBI6#079<?@9<6GH6#O7BI?@GR6#079<6yDC4705]#;4707?VO#BIEF6#^`BI;#076BI07O#BIa7BIO#47?@9M?O#?V470a767EF8:;#EF607g«8:6 DC?DC;#EJ;9<6#GRA76#EJ?@9<47EF?8LB9<EJ;#a7?V8:;#9<9<;yDC?9<6#GHA767EF?@9<47EJ?VO#BZ9<EF?@078jBI^_BC;#076y076#GR?@9<BI=@;7¬ BC8:;#9<EJ;#A7;®¯Id±°6#E²9<6#GHA767EF?@9<47EJ6-GH?@]#]7BC;#EJBO#B>¯QgBID±=@EJBC8:9M?@DIDC;-DIBI2747BIO7;-8LB

(3) 9<EF;#a7?@g BC07a56#=@6#gBI0cb<?@8:6²BI8:;#9<EF;#A7?@gBI0c=@47BoDC6²;7EFBI6#079<?@^`BC;#05BoO#67DCDI6²GR;#DC67=@;#DC6c8L;707;²O#6#Do9<479<9<; =@?@8:47?LDCBPSU³oBI]#47EJ?y´_d ´`[<d. µ:¶ · ¸¹<º±»½¼p»_¾À¿Á1ÂÄÃ7Å Â1Á Æ½Á1ÅÇ5ÈsÉÊÈ Ë ËÄÈÌÅËÄÈ ÍFÅË1ÈTÇ5È Ë Ë1ÎuÏ ÎFÂÀÈÇ7ÈÌ

(4) ÎJÐ Á1ÍFÎÈTÁ ÇHÑ ÒÊÈË ËÄÎuÁ1ÂJÅÊÐ ÓÊÅUÃ7ÎFÔFÕ ËZÖUÈÊÐCÐCÅ ÓFÈ× Á Ç7ÉÁÀÖIÁÄÉ ÒÊÎKËÄÎZÉ Á ÓFÈÆÀÁÄÅÇ5ÈoÌÈ_ÉUÁ1ÎKËÄÒ<Ç Ø#Å\ÍJÒUÁÂ1ÁÉÁ1ÂÄÃ7ÅUÇ Ø7ÅUÇ7ÅËÄÈuÌ±ÅËÄÈ ÍFÅË1ÈoÁ Ç\Ï½ÎJÂÀÈoÇ5È Ì

(5) ÎÀÐ ÁÄÍFÎFÔ °;#BI=@N7ÙÚDC?Úb<?@8L60767GR?L9<BC=@??@A7A7?@EF69<;#EJª#BCO#?Ú?@DCDI;8:]#47?@EFO#;7g-GH6#059<EF625476#DIDC? BC8:;#9<EJ;#A7?Û?@A#A7?@EJ6c9<EF?@8:A7?5EJ6#079<6#guDC?Û9<6#GRA76#EJ?@9<47EF?ÛO#Bu9<EF?@078:BI^`BC;#076Ü ¯ 3O76#9<9<?h?@07=@N76 #sÝo_Lu<¦:h§7u@Þ7QLIß<I@@àÌá_@d CAPITOLO 1. 1.

(6) om npmunpm âM}z#{Êxpt5|v#}p}pry}CxÄ~PxCKrãoq\ä /10325476#8:9<;>DC?@a7;7EF;>O#BK9<6#8:BK h8:9<?@9<;>458:?@9<;>BIDK=@;#GRA7;#8:9<;åæJÝ_\ I¤ æLåç æL@Iá#è#Iß<_I¤CLg BC07O7BC=L?@9<;-ª#EJ6#a76#GR6#079<6-=L;#0DI?é8:BC]#DI?éWXZYZgO#B

(7) =@45BEJBCA7;7EF9<BI?@GH;-DI;-8:=@N76#G?éO#6#DIDC? GH;7DC6#=@;#DI?fBI03³oBI]#47EF?V´`dIêd ö?hDI4707]#?f=@?@9<6#07?f?@DQBCb<?@9<BI=L?hXsëÄìRííKO#6#9<6#EÀGHBI07?fDC?hb<;#EJGR?Û?@DQDI4707]#?@9<?hO#67DIDC?fGR;#DQ6#=@;#DI?Lg GH67079<EF6!BIDhDI6#]#?@GR6l9<EF?BÛO#476!]7EF47A7A7BÛ?@EJ;#GH?@9<BI=LBÛ076l?@8:8:BQ=@47EF?DI?iEJBI]#BCO7BQ9<î`dÛö? GH;7DC6#=@;#DI?O#BWXZY!N7?4707?DC4707]7N76#^`^j?O#B=@BIEF=@?êï#ð&6é4707?DI?@EF]N767^j^`?O#B=@BIEF=L? Wð\d/ÄD=@;#GRA7;#8:9<;W#XZYiBC0b<?@8:6076#GR?@9<BI=@?y 470GR6#^`^`;;79<9<BC=@?LGR6#079<64707BI?@8:8jBI?@DC65g =@;#0ñ4707?Ü9<6#GRA76#EF?@9<47EJ?ÜO7B±9<EF?@078jBI^`BC;#056O#?LDCDI?Üb<?L8L6056#GH?L9<BI=L?Ü?é25476#DIDI?òBI8:;#9<EJ;#A7? A7?@EFB?Ü¯óô#WdIôVõFXZd°;#BC=@N7Ù>DI?3GR;#DI6#=@;#DC?3O7BTW#X«YA5EF6#8:6#079<?@gDI4707]#;BIDT8:45;²?@8L8:67g 470bU;#EJ9<6GR;#GR6#079<;O#B«OBIA7;#DI;6#DI6#9<9<EFBI=@;O#;a7479<;?@DCDI?A5EF6#8:6#07^`?O76#D«]#EF47A7A7;XZ©g DC?.GR;#DI67=@;#DI?.07;#0 %8:BQGRGH6#9<EJBI=@?%A76#EBI07a76#EJ8:BC;7056i8:A7?@^`BC?@DQ6#dH479<9<?@a7BI?LgHBI0b<?@8:6 076#GR?@9<BI=@?DC6GR;#DC67=@;#DC68:B\;#EJBC6#059U?@05;ÜGR6#O7BI?LGR6#059<6ÜBI047]#47?@D\0745GR6#EJ;Ü056#DCDI6òO#476 O#BCEJ6#^`BC;707Bo6#go2747BI07O#BQg?ÛDIBIa56#DCDI;²GR?@=@EF;#8:=@;#A5BC=@;#goDQ?38:BIGGH6#9<EJBI?38:458:8jBI8:9U67doögoBI07;#DI9<EF67g A7EF6#8:6#059<6470.O#BIA7;#DI;6#DI6#9<9<EFBI=@;A76#EJGH?@0767079<6076#D8:6#078:;O#6#DQDI?-DI?@EJ]#N76#^`^`?-O#6#DIDI? GH;7DC6#=@;#DI?@gPGH?f fGH;7DC9<;3GRBI07;#EF6>O#BP27476#DIDI;>A7EF6#=@67O76#079<6#d. µ:¶ · ¸¹<º»½¼ ÷¾½øÅUËÄÈ ÍFÅË1Î«ÉUÁù`ú_û °;#BI=@N7ÙDC?b<?@8L6076#GR?@9<BI=L?y y4705BC?@8:8jBI?@DC67g9<479<9<BBA5?@EF?@GR6#9<EFBG?@=@EF;#8:=@;#A5BC=@B«;#9<9<BI=@BIg 6#DC679<9<EFBI=LBCg6GR?@]#076#9<BI=LBTN5?@0707;O#476a7?@DC;#EJBO#BCa767EF8:B076#DIDC?>O#BIEF67^jBI;#076A5EFBIa7BCDI6#]#BI?@9<?>6 8:47DA7BI?@07;é?ò2747678:9<?ò;#EJ9U;#]#;07?LDC6#dsX«;70éBIDA767O#BC=@6éü ||?@=@=@?@079<;é?@D8:BIGRª#;#DI;ñO7B470 A7?@EF?@GR6#9<EF;7gBC07O7BC=@N767EF6#G;ò=@N76ò2747678L9<;8:BEFBIb<6#EJBC8:=@6?@DCDI?O5BCEJ6#^`BC;#076A7EJBCa7BIDI6#]#BI?@9<?@g GH67079<EF6=@;#0BIDA76#O#BI=@6ü ⊥076BC07O7BC=@N76#EJ6#GR;4705;=@N76]#BI?@=@6DI4707]#;DC?O#BIE6#^`BI;#076 ?@O>678:8:?hA767EFA76#07O7BC=@;#DI?@EF67d °6#E±BCDWXZYñ8:BN7?3=@N76DII?@07BI8:;#9<EJ;#A7BC?3O#BC6#DQ6#9<9<EJBC=@? >A5;#8:BC9MBIa7?>62747678:9<;²b<?>8:ý =@N76#gþ8:;#9<9<;ÿDII?@^jBI;#076ÿO#Bþ470 =@?@GRA7; 6#DC679<9<EFBIε=@;#−gþε DC? GH;#DI6#=@;#DI? 8:B&;#EJBC6#059<B A7?@EF?@DIDC67DC?@G6#079<6V?@DT=@?@GRA5;#d ?@DA747079<;O#BTa7BI8:9<?cGR?@]#076#9<BI=@;#gDI6VGR;#DI6#=@;#DI6VO#BTWXZY 8:;#07;VO#BI?@GR?@]#076#9<BI=@N76#gT=L;#04707I?@07BI8:;#9<EF;A7BI?cO#67DCDI?>8:478:=@6#9<9MBCa7BI9<îhGR?@]#076#9<BQ=@? χ ó χ GH?@]7]#BC;7EF6%O#B^`6#EF;s2747BI07O#B6#8:8:6-8:B;#EJBC6#059<?@05;%A7?@EF?@DIDC67DC?@GR6#079<6%?@05=@N76%?@D − χ =@?@GHA7;>GR?@]#07679<BI=@;#d ||. ⊥. ||. ⊥. mon Z{ r{ xpK| hKx PrP}Ä3KxTt5 P{

(8) xpz7xCyPK}C}pv

(9) v7t5ywK>v#|xpz#v mon npm

(10) xp{ K||UrK{ÊyPv#{ v73u|<{ ryCru{ÊKxpw °6#E-O76#8:=@EFBIa76#EF6 2747?@059<BC9<?@9<BIa7?@GR6#079<6 DI?(b<?@8:6&0767GH?@9MBI=@?@g8jB?@8j8:;#=@BI? ?LO ;#]#07B GH;7DC6#=@;#DI?l470 a767EF8:;#EF6®?l;#EFBI6#079M?@9<; =@;#GH6(BID>8j47;®?@8:8:6(DC4705]#;#d6#b<BI07BI?@GH; BID a76#EF8:;#EJ6l07S EJ[UgfO7BCA76707O#67079<6iO7?@DCDQ?.A7;#8:BI^`BI;#076kEFgR=@;#GR6BCDRa76#EJ8:;#EF6GH6#O7BI;iO76#DCDQ6 ;#EFBI6#079<?@^`BI;#07B ?c8:44707?cEJ67]#BC;7076VO#BT076#GR?@9<BC=@;=@67079<EF?@9<?cBI0E6VO#BTa7;#DI47GR6V]#EJ?@07O#6 EFBI8:A76#9<9<;-?@DCDI6-O#BIGR6#058:BC;705BGR;#DC67=@;#DC?@EJB6-A7BI=@=@;#DQ;-EFBI8:A76#9<9<;-?@DIDC6-O#BIGR6#078jBC;707BO#6#D 8:BC8:9<67GR?@dñ/ÄDña767EF8:;#EF607S EF[ =@N7BI?@GH?@9<;§# LT< á_:6#gñA767E DI?A7EF;A7EJBC6#9<î¡O7B CAPITOLO 1. 2.

(11) 8:BCGGH679<EFBQ?A767E BC07a767EF8LBI;#076 8:A7?@^`BC?@DI6 O#6#DQDC? b<?@8:6 076#GR?@9<BI=@?Lgi8:;#DI; DI?8:45? O#BCEJ6#^`BC;7076> fEFBIDI6#a7?@059<6#BPa76#EF8:;7EFB05S EF[Z6c¬o07S EJ[ 8:;#07;#gK?@DCDI;#EF?@gK6#2747BIa7?LDI6#079<BCd °6#EO#6#8:=@EFBIa76#EJ6c2747?@079<;>DI6cGR;#DC67=@;#DC6>8jBI?@07;c?@DIDIBI056#?@9<6cDI4707]#;cDI?hO#BIEF6#^_BI;#076cGR6#O7BI?@g 8:B BI079<EF;7O#47=@6yBIDuÝL@T Lá§sç á_L§# £L@@¤IL S EÀ[Ug ?@07=@N7C678L8:;O#BIA76#07O#6#079<6O#?@DIDI? A7;#8:BC^`BI;#076#g O#67bUBI07BI9<;yBI0GR;#O#;=@N76ya7?@DI]#?é´Û076#DZ=@?@8:;yO#B G?@8:8jBCGR;y?@DQDIBC0767?@GR6#079<;7g =@BC;# h2745?@07O#;>DI?ÛO7BCEJ6#^`BC;#076²?fO#BK;#]#07BKGR;#DC67=@;#DC?h=@;7BI07=@BIO#63=@;#03DI?hO#BCEJ6#^`BC;#0563GH6#O7BI? 07S EF[UgK6>a7?@DI]#?fïcBC03b<?@8j63BQ8L;79<EF;#A7?@d °6#ERO#6#b<BI07BIEF 6 gZ=@;#078:BIO76#EFBI?@GR;4708:BI8:9<6#G?VO#B =L;#;#EJO#BI07?@9<6A7;7DC?@EJB«8:b<6#EJBI=@N76#gZ=@;#0 ?@8:8L6A7;#DI?@EF6SU;^j6707BC9<?@DI6#[A7?@EF?@DIDC67DC;?07S EJ[Ug68:BC?@07; 6 EJBC8:A76#9<9<BIa7?@GR6#079<6]#DCB ?@07]#;#DIBA7;#DI?@EF6é6é?@^`BCGR459M?@DI6#d/Ä079<EF;7O#47=@BI?@GR;éDI?b<4707^`BI;#θ076éO#φBO7BI8:9<EFBIª#45^`BI;#076ßÄS θg φ[ O#6#b<BI07BC9<?ÛBI0cGR;#O#;²=@N76ßÄS g [UO 8:BI?ÛDC?3A7EJ;#ª#?@ª#BIDQBC9MîH=@N76²DI?3O7BCEJ6#^`BC;7076²O#67Dua76#EF8:;#EJ6 ?@g²BC0®470®O#?@9<;&A747079<;þO#θ67φDCDI; Ω8LA5?@^jBI;#g8:BI? =@;7079<6#07479<?(076#DIDCI?@07]#;#DI; 8:;#DCBIO#; O Ωg =@6#079<EF?@9<;BI079<;#EF07;?@DIDC?O#BCEJ6#^`BC;#056S θg φ[UdöIBCA7;79<6#8:BO#B«8:BIGRGR6#9<EJBI?y=LBIDCBI07O#EÀBC=L?O#6#DIDI? b<?@8:6%076#GR?@9<BI=@?ñ?@9<9<;#EJ07;%?@DO#BIEF679<9<;#EF6%BIGHA5;#076%=@N76ßH07;0-O7BCA76707O#?ñO#?@DIDCQ?@07]#;#DC; ?@^jBIG479<?@DC6 φ 67gfA5;#BC=@N7Ù%DC?%O#BIEF67^jBI;#076O#Bh?% 6 :?% %DI?%8:9<678:8:?LgÛßÄS [Uóß1S ¬ [Ud KB O#6#b<BI07BC8:=@6 >=@;#GR63BIDKGR;#GR6#079<;>O#BP2747?@O#EJ47A7;#DI;>O#6#DIDC?fO#BI8j9<EFBIª#47^_BC;7076θß π θ S=. 1 3 cos 2 (ϑ ) − 1 = π 2. π 0. (. ). f (ϑ ) 3 cos 2 (ϑ ) − 1 sin (ϑ )dϑ. SÊ´`d´`[. ©6#Do=@?@8:;²O#BoGH?@8j8:BIGR;²?@DIDIBC076#?@G6#079<;7g8:BoN7?3=@N76 K=@;78 ó-´_g62547BC07O7BTDI?3SÊ´`d´j[ b<;#EF07BI8:=@6²óé´`du°o6#E

(12) DI?hbU?@8:6>BC8:;#9<EJ;#A7?@gKBC07a56#=@6#gu8:BPN7?!Kθ=@;#8 θ óé´#"ôgK6c2#47BI07O#BK8:B ;#9<9<BC6707$ 6 ólï&d %0.?@DI9UEF;=@?@8:;07;79<6a7;#DI6 -2#476#DIDI;BI0.=@47BRDI6GR;#DI67=@;#DI68:;#07; ;#EFBI6#079<?@9<6l9<479<9<6!;#EJ9<;#];07?@DIGR6#079<6l?@D3O5BCEJ6#9<9<;#EF6 BC0k9<?@DÛ=@?@8:' ; K=@;#8 θ ó®ïgÛ6 2747BI07O#(B có¬« ´ "Uêdu©6#Du=@EFBI8L9<?@DQDI;cDCBI2747BIO#;cWXZYZgKBCDKA7?@EF?@GR6#9<EF;>O#C;7EFO#BI07) 6 ²O765=@EF6#8:=@6 ?@DCDII?@45GH6#059<?@EF6O#67DCDQ?.9<67GRA76#EF?@9<47EJ*? kEJ?@]#]#BI4707]#6i450a7?@DI;#EF6iGBI07BCGR;iO7BH=LBIEF=L? ïdIêôòSU?@DCDI?9<6#GRA76#EJ?@9<47EF?yO#B=@N7BI?@EFBIb<BC=L?@^`BI;#076#[UgA7?@EJ9<6#07O#;O#?y470a7?@DI;#EJ6òGH?@8:8jBCGR; O#Bu=LBIEF=@?fïdIWc?@O>4707?f9<67GA76#EJ?@9<47EF?hO#BKêïõFXZd mon n Kwt5xp| ÛKxKwP{,+KxpvcK}pv#t5|xpz#v öI6#076#EJ]#BC?O#QBC079<6#EJ?@^`BC;#0769<EF?O#476GR;#DI6#=@;#DI60767DCDQ?Vb<?@8:60767GH?@9MBI=@?LgZ8:607;#08:;#07; 8:;#]#]#6#9<9<6²?3=@?@GRA7Bo6#8:9<6#EF07BIgo 3GHBI07BQGH?32745?@07O#;²BIDTO#BIEJ6#9<9<;#EF6² 3;7EFBI6#079<?@9<;;a7450727476 076#DIDC?f8:9<6#8:8j?hO7BCEJ6#^_BC;#056#gK=@BI;#* 07S EJ[Zó.0 SÊ´`dIê[ ©6#DIDC?A7EF?@9<BI=@?LgBCD«=@EJBC8:9M?@DQDC;DIBC2747BIO#;A74 /y678:8L67EF68L;79<9<;#A7;#8:9U;?@DCDIC?@^`BI;#076O7B=@?LGHA5B 6#8:9<6#EF07Bo6#O² 38j6#GRA7EJ6²O#6#DIBCGBI9U?@9<;cO#?3470c=@;#079<6#05BC9M;#EJ6#g=@N56²BC059UEJ;#O#47=@6c4707p67076#EF]7BC? O#CBI079<6#EJ?@^`BI;#076®=@;#0 DI6&8:476®A7?@EJ6#9<B h076®8L67]#476®=@N76#g²076#DIDI?(=@;#07b<BC]#47EJ?@^`BC;#056 O#B 6#2747BIDCBIª#EJBC;8:9<?@ª7BIDC65g!BIDl=@?@GRA7;O#BIEF6#9<9<;#EJ6EFBI8:47DC9<?@059<6A74 / O#BCA56#07O#6#EJ6O#?@DIDC? A7;#8:BC^`BI;#076²EsBI03GR;#O#;>07;#03ª7?@07?@DC6#d /103]76#076#EF?@DI6#gKDI?hb<4707^`BI;#076 O#65DCDIC67076#EF]#BI?fDCBQª#6#EJ?f=@;#079<6#EFEJîRBK8:6#]#476#059<BK9<6#EÀGHBI070B öI6#076#EJ]#BI?ñDIBIª#6#EF?ÜBI079<6#EF05?@g?@8:8:;#=LBC?@9<?é?@DIDII6#0767EF]#BQ?éO#BBI079<6#EF?@^`BI;#076-9<EF?éDI6 • GH;7DC6#=@;#DI6#gZ=@N76y VDQ?V8:;#GRGH?O76#DIDCI6#076#EJ]#BC? -O767DCDI;8:9<?@9<;y07;#0yO#BI8:9<;#EF9<;6 O#6#DIDCI6#076#EJ]#BI? 1325476 O#;#a5479<?h?@DIDIC67a76#079<47?@DI63O#BI8:9<;#EJ8:BI;#056T öI6#076#EJ]#BC?òDIBCª76#EF?ò678:9<6#EF05? 89476 g?@8L8:;7=@BI?@9M?ò?@DCDIQBI079<6#EJ?@^`BC;#076ñ=@;70ñB=@?@GHA7B • 6#8:9<6#EF07B CAPITOLO 1. 3.

(13) o¨ I6#076#EJ]#BC?O7BsBI079<6#EJ?@^`BI;#076 47:3; 9<EJ?BIDs8jBI8:9<67GH?056#GR?@9MBC=@;Ü6ÜDI6Ü8:47A767EFb<BI=@B =@N76>DC;>O76#DIBIGBC9<?@07;7d K60a7?@EFBI?¢?@A7A7EJ6#^`^j?@ª7BCDIGR67079<6 8:44707?¢O7BC8:9M?@07^`?=<]#EJ?@07O#6 EÀBC8:A76#9M9<;Ú?@DCDI6 O#BCGR6#078jBI;#07BGR;#DC67=@;7DC?@EJBCgoA7;#8:8:BI?@GH;458L?@EJ6²DI?Ü #á_LI>§##¤o@á_\ \¦ áuP8:6#goBI07;#DC9<EJ6#g(< ²]#EF?@05O#6?@07=@N76VEFBI8:A76#9<9M;?@DEF?@]#]7BC;VO#C?@^_BI;#076O767DCDI6b<;#EJ^`6BC059<6#EFGR;#DI6#=@;#DI?LEFBSU=@N76 -O#BRA5;#=@N76DI4707]#N76#^`^`6GR;#DI6#=@;#DI?@EFBI[UgRA7;78L8:BI?LG;478:?@EF6DI?® #á_:C-#¤Q@£ C@éA56#E O#6#8:=@EFBIa76#EJ6DII6#076#EJ]#BI?>DIBIª76#EJ?>BC079<67EF07? ? >½.´ @½d°;#8j8:BQ?LGH;#g?@DIDC;#EJ?@g8:=@EJBCa767EF6²DIC65076#EF]#BI? DCBIª#6#EJ?hBI079<6#EJ07?f=@;#GR6 SÊ´`dIô[ A BDC 8E4F6*C 47:3;GC 83HJI O#;#a76 8KH5I þDCI6#0767EF]#BI?¡#¤C@£P I@®O7BO7BI8:9<;#EJ8LBI;7076#d©6#DIDI?þ9<6#;#EFBI?&6#DI?@8:9MBI=@?@gBI0 ?@07?@DC;7]#BC?é=@;#0DI?é9<6#;#EFBI?éO#B±ìs;#.; L76-O#67B8:;#DIBCO7BCg

(14) 8LB±=@6#EF=@?é4705C6#8:A7EJ6#8:8jBC;#056-O#6#DIDC? O#6#078:BI9<î-O7Bh6#076#EF]7BC?6#DC?L8:9<BI=L?A76#E4707BI9<î-O#Bha7;#DC47GRN 6 MO P Q8:;#9<9<;lb<;#EJGH?O#Bh4707; 8:a7BCDI47A7A7; BI0 8:6#EJBC6 O#B>\S? RDI;#EFg0767DCDI6 A7;#9<6#07^`6 O#B ∂nα SU=@;#0 αg β U ó T7Jg V@gÄà [Ug ?@EFEF678:9U?@9<;ñ?@BsA7EFBIGHBs=@;#079<EFBIª#479<Bs8LBI]#07BIb<BI=@?@9<BIa7BId/=L;#6#b<b<BC=@∂βBI6#079<BO#B2747678L9<;ñ8ja7BIDC45A7A7; 8:;#07;DI6=@;78:9<?@079<B«6#DC?@8:9<BQ=@N76=@N56O#6#8:=@EJBCa7;707;BID8:BC8:9<67GR?@d«6#076707O#;=@;7079U;O76#DCDI6 A7EF;A5EFBI6#9<îfO#BT8:BIGRGR6#9<EJBI?>O#67DCDI?>b<?@8:60767GR?@9<BI=@?@go8:BoEFBI=@?@a7?>DCI678:A7EJ6#8:8LBI;#076²;#9<9<6#07479<? O#?h³oEJ?@0 LW>Äê @\6>EÀBC67DC?Lª#;#EJ?@9<?hO7G? XEJBCS= L78:67W 0 >Äô#Zg Y(@# •. MO[P Q. =. [. 1 2 2 2 K 11 (∇ ⋅ n ) + K 22 (n ⋅ ∇ × n) + K 33 (n × ∇ × n) 2. ]. SÊ´`d\Y[. 74 6#8:9<?òb<;#EFGR47DI?Ü678:A7EJBCG6ñDI?§# £j ]y£FÝo@àjQ@¤IòO7B

(15) 6#076#EJ]#BI?Ü6#DI?L8:9<BI=@?ò6#Oé ò07;#9<? =@;#GR6__FCf¤IIè# Lh7¤Q@£K Q@f§#*M@L^Pd _ 8:8L67EFa7?@07O#;iDC?.SÊ´`dZY[Ugh8:BhA74`/07;#9<?@EF6i=@;#GR6k=LBI?@8:=@4507?=@;#8:9<?@079<6k67DI?@8:9MBI=@?8jBC? ?@8:8L;7=@BI?@9<??@Oé4707?A7?@EJ9<BI=@;7DC?@EJ6ñO76#b<;#EFGR?@^`BC;7076éO76#D=@?LGRA7;éO#BCEJ6#9<9<;#EJ6#ad X8:BI8:9<;#07;#g BC07b<?@9<9<BIg]#67;#GH679<EFBI6&=@N76®EJ6#?@DCBI^`^`?@07;&450 8:;#DI; 9UBCA5;&O#B²O#6#b<;#EJGH?@^`BI;#076TÛ27476#8:9<6 ]#6#;#GR6#9<EFBI6>8:;#07; ö; £JÝ¤IS V5g!=@?@EF?@9<9<6#EÀBC^`^_?@9<; O#? ∇ ⋅ n ≠ 0 g ∇ × n = 0 6 O#?@DIDI? =L;#8:9<?@079<6 • 6#DI?@8L9MBI=@?fO#BK8:A7DIS? Rb

(16) íí /ÄD

(17) K cZC£P gu=@?@EF?@9<9<6#EJBI^`^`?@9<;cO#? ∇ ⋅ n = 0 g (∇ × n)|| y6²O#?@DIDI?3=@;#8:9<?@079M6²6#DI?@8:9MBC=@? • O#BuK9 d

(18) BC8:e9 b /ÄDTè#_o§@gu=@?@EJ?@9<9<67EFBI^j^_?@9<;>O#? ∇ ⋅ n = 0 g (∇ × n)⊥ V6>O#?LDCDI?h=@;#8:9M?@079M6>6#DI?@8:9<BI=@? • O#Buª76707O bgf0fF /10³oBI]#47EJ?®´`dCôl8:;#0#;iGH;78L9<EJ?@9<6k2747678L9<6i]#6#;#GR6#9<EJBC6i6kDI6kBI079<6#EF?@^`BI;#07Bf?LOk6#8:8:6 ?@8:8L;7=@BI?@9<6#d. CAPITOLO 1. 4.

(19) K33. K11. K22. ∇n. ∇× n||n. ∇×n⊥n. µ:¶ · ¸¹<º» ¼ h#j¾ i Â1Á Ç ÁÄÂÀÐ ÓlÎ kRÂJlÍ m7ÈÌ

(20) Î²ÉÊÈ Ë ËÄÈ3Ø5È_ÅUÌÈ Ð Ó<ÁÄÈÉ ÁRÂpÃ ËÄ3Î n k&o_ÈUÇ5ÉyÈFÐ p Á1ÂÀ\Ð q ËpÈÛÏCÓÈ_ÍÀÍFÈÛÇ7ÈÓFÈ Á Ç7ÉÁ1ÍJÎMÇ7Å«ËÄÎ\É Á ÓFÈ Æ Á1ÅÇ5È±ÉÊÈØ_Ë ÁÎFÂJÂÄÁ7Ï ÎFÍMÁ Ë ÁÂÀÒUË ËpÈÂÀÒUÃ7ÈÓMÏCÁ1ÍMÁoÈZËÄÈZË Á Ç5È È

(21) Ð ÓÎJÐCÐIÈØ Ø Á1ÎFÐIÈZÁ Ç7ÉÁ1ÍJÎMÇ7Å Ë1ÈZË Á Ç5È È É Á ÏÅ Ó<Æ`ÎÛÉ ÈË

(22) ÍFÎMÌ Ã7ÅcÉÁ ÓFÈ ÐIÐCÅÓÈ Ô iiÉ È ÂÀÐ Ó3Î k ÓÎMÃ Ã ÓFÈ_Â½ÈÇ5ÐpÎ1ÆÀÁÄÅÇ5È²ÂJ3Í m5ÈUÌ±ÎJÐ Á1ÍFÎÛÉ È Ë Ë1È²ÂÀÅË ËÄÈ Í1Á1ÐCÎMÆÀÁÄÅÇÊÁ Ì±È ÍJÍFÎMÇ Á1lÍ m7È\Â½,Ò oUÁÄÐCÈÉ ÎMË ËÄÈoÌ±ÅUËÄÈ ÍFÅË1ÈoÇ5ÈË Ë1ÈÐ ÓFÈØ5È ÅÌÈ Ð Ó<ÁÄÈJ¼ öBI079<6#EJ6#8:8L?@059<6>DC?ÛA7;#8:8:BQª#BIDCBI9MîHO7Bu8:9MBCGR?@EJ6>BCDua7?@DI;#EJ6cO#6#DIDI6>=@;#8:9<?@079<Bu67DC?L8:9<BI=LN76c=@;#0 470lEJ?@]#BC;707?@GH67079<;(A747EJ?@GR6#079<6!O#BQGR6#078:BC;707?@DCj6 A7;#BI=@N7ÙiDI?iO#6#078:BI9<î%8:A7?L^`BC?@DI6!O7B 6#076#EJ]#BC?yN7?DI6O7BCG6#078:BI;707BO#B4705C6#0767EF]#BI?A767EÛ4@07BC9<îO7Ba7;#DI47GH67gDC6=@;#8:9M?@079<aB ber r N7?@0707; DC6®O#BIGR6#078:BC;707BcO#B²4707I6#076#EJ]#BI?(O#BIa7BI8:?!A76#E4705?(DI470#]#N767^j^`?@d²üC67076#EF]#BI? =@?@EF?@9<9<6#EJBI8:9<BI=L?BI0]#BI;#=@; yDI?A7?@EF9<6?@07BQ8:;#9<EF;#A7?yO#6#DIDCI6#0767EF]#BI?O#B«BI079<6#EJ?@^`BQ;#0769<EF? DC6éGR;#DI67=@;#DC67gs=@N76éa7?@DIt 6 svu ïd´`6#e\g\GH6#059<EF6éDC?DI4707]#N76#^`^`?ò=@?@EJ?@9<9M6#EFBI8:9MBI=@? DC? DC4705]#N76#^`^`?ÛO76#DCDI?hGR;#DC67=@;7DC?> u-êïðdu©6>8:6#]7476>=LN76>8:9<BCGRBQ?@GH; b r r uws /& u!´`ï x íí ©g=@N76 y6#b<b<6#9<9<BIa7?@GR6#079M6DCI;#EJO#BC076O7B]#EJ?@07O#6#^`^_?GBI8L45EF?@9<;A76#Eh?@DI=@4707B«=@EFBI8L9<?LDIDIB DCBI2747BIO#B07í 67GH?L9<BI=LB9MBIA7BI=@BIzd yO%í 6#8:6#GRA7BC;7g?(óiêíW#õFXZgA56#EVBIDWXZYZg8:BN7W ? b

(23) í{í u | dI( ê }1´j*ï x ©sg b 0 uô\d ~(}1´`*ï x ©.6 bgf0fudI(ô }1´`*ï x ©d om n pxpwP|UP{_v@xCrKwyz7ruwVxTz#v7 xTPt5| K{ wPxFPuwK{+Kxpvc>v+Kwu|xpz#vcPP}pK||{ÊxÄz7v /10+25476#8:9<;¡A7?@EF?@]#EJ?@b<; O#6#8:=@EJBCa76#EJ6#GR;+By=@;#079<EJBCª7479<By?@DIDC? O#6#058:BI9<î(8:A7?@^_BI?@DC6+O7B 6#076#EJ]#BC?ÛDIBCª76#EF?ÛA7EJ;#a7607BI6#079<BuO#?@DIDCQBC059U67EF?@^`BC;7076cO#67DIDC?Ûb<?@8:6c0767GH?@9<BQ=@?Û=@;#0>BIDu=@?@GRA7; 6#DC679<9<EFBI=@;>;3=@;#0327476#DIDC;>GR?@]#07679<BC=@;#d mon npm

(24) uwt@xp|0hKxuwP{,+Pxpv²}pxZKP{ vc>v+uwu|xpz#v /1DfO#BIEF679<9<;#EF6iO#Bf470i=@EFBI8:9<?@DCDI;kDIBI2747BIO#;kA74 /a5?@EFBI?@EF6kDI?8:47?;7EFBI6#079<?@^`BC;#056k8:;#9<9<; DCI?@^`BC;#056ÜO7B470=@?LGRA7;òGH?@]7076#9<BC=@;7d 476#8:9<;?@=@=L?@O#6ÜA56#EF=@N7Ù@g\BI0b<?@8L6ò0767GR?@9<BQ=@?@g 07;#0é8:;07;ñ4#]#47?@DIB

(25) DI6ñ=@;#8:9<?@079<B

(26) O#Bs8:478:=L6#9<9<BCa7BI9<îyGR?@]#07679<BC=@? 6 SU;#g

(27) BC0éGR;#O#; 6#2747BIa7?@DC67079<6#gDC6V=@;#8:9<?@079MB O7B A56#EFGR6#?@ª7BIDCBI9MîÛGR?@]#076#9<BI=@?²EF6#DQ?@9<χBIa76 µχ 6 µ g=@;#0 χ ó ´>6 χ ó µ − ´j[UgZGRBC8j47EF?@9<6yA7?@EF?@DIDI6#DC?LGR6#079<6y6y;#EJ9<;]#;#05?@DCGR6#079<6y?@D«O7BCEÀ6#9<9<;#EF6#d µ − ö?fGR?@]#076#9<BI^`^`?@^`BI;#076 BC07O#;79<9<?ÛO7?h4503=@?@GRA7;>G?@]#076#9<BI=@;cì- hO#?L9<?@gKA56#EF=@\B /@gKO#*? ó ì !S χ − χ [US ì }07[«0 SÊ´`dIW[ χ GH67079<EF6>DI?hO76#078jBC9<îO#BP6#076#EF]7BC?hDIBIª#67EF?fGH?@]7076#9<BI=L?h * ||. ⊥. ||. ||. ⊥. ||. ⊥. ⊥. CAPITOLO 1. ⊥. ||. ⊥. 5.

(28) −. 1 Yv} ì%ó 2. −. ||. ⊥. 1 - > 1S µ µ⊥ ( µ|| 2 2. − µ⊥. [US ì}07[@. SÊ´`d | [. /1D8L67]#07;òü −ü\056#D\GR67GHª7EJ;ò?8:BI07BI8:9<EJ?O#67DIDI?SÊ´`d | [9<BC67076Ü=@;7079<;ÜO76#D\DQ?@a7;#EF;òb<?@9<9<; O#?@DH]#6#076#EJ?@9<;#EF6iA56#EG?@079<6#0767EF6i=@;#8:9<?@079<6BCDR=L?@GRA7;iGR?@]#076#9<BI=@;iSUa76#O767EF6#gH?@O 6#8:6#GRA7BC;#gsEF6#b<d>ÄW@À[Uds/1DsA7EFBIGR;ñ9<6#EJGRBC076éO#6#DsGH65GHª#EJ;é?òO#678:9UEJ?O#6#DIDI?SÊ´`d | [R07;0 O#BCA56#07O#6þO#?@DO5BCEJ6#9<9<;#EF6þ6#gV2747BI07O#BIg07;#0& ®BC07b<DI476#07^`?@9<;þO#?@DIDI?®O#BQ8:9<;#EF8:BQ;#076#dV/1D 8:6#=@;#07O#;9<67EFGRBC0767gBI07a76#=@6#gb<?@a7;#EJBC8:=@6470%?@DIDIBC0567?@GH6#059<;O#BH0%A7?@EF?@DIDI6#DQ;?@Oiìg A7;#BI=@N7Ù µ − µ ó χ − χ ï 076#B>=@EJBC8:9<?@DIDIB3DIBI2747BIO#B>0767GR?@9<BI=@BQ d yB>b<BC0@B>O#6#DIDI? GHBI07BQGHBI^`^`?@^`BI;#076 O#67DIDCI6#056#EJ]#BI? DIBCª76#EF?(9<;#9<?LDI6#gA7;#8:8:BI?LGH; O#6#b<BI07BIEF6#g²O#470527476#g²DC? O#6#078:BI9<î¡O7Bñ6#076#EJ]#BC? DCBQª#6#EJ?GH?@]7076#9<BI=@? GH?@059<67076#07O#; 8:;#DC; BCDñ9<6#EJGRBC076 =@N76 O#BCA56#07O#6>O#?@DPO7BCEJ6#9<9<;#EJ6 ó 1 -S [US ì }07[ SÊ´`\d [ F mag − µ χ −χ ||. ⊥. ||. 2. ⊥. ö?¢2745?@079<BC9<î χ − χ a7BI6#076BC07O5BC=@?@9M?¢=@;#0 χQ6#OÚ O#67b<BC07BI9M?ÚQ£jáT Lá`ÝI H7T C@` d yDIDI?kSÊ´`d\[y=@;#EFEJBC8:A7;#05O#6 4705?lO#6#078:BQ9<î8:A7?@^`BI?@DI6(O76#D3GR;#GH65079<; O#B b<;#EF^`?h6#8:6#EF=@BI9<?@9<;3O#?Ûì-8j47DuXZü©gPO#?@9M?hO7?* ó µ- χQ S 0 }ìs[ZS 0 × ìs[ SÊ´`d\[ τ l _ 8:8L67EFa7BI?@GH; =@N76BIDñG;#GH67079<; 0547DCDI;A76#Eþ0ÚA7?@EF?@DIDI6#DC; ?@Oì 6 A76#E 0 A76#EFA76707O#BI=@;#DC?@EJ6>?@Ocì-d mon n

(29) uwt@xp|0hKxuwP{,+Pxpv²}pxZKP{ vcK}Cu||U{ xpz#v DCB

(30) 6#b<b<6#9<9<B±O5B±470ñ=@?LGRA7;6#DC679<9<EFBI=@;-8:47D=@EFBI8:9M?@DCDQ;DCBI2747BIO#;8:;#07;#g

(31) ]#6#076#EJ?5DCGR6#079<67g A7ZB h=@;#GRA7DI6#8:8jBCdP°;78L8jBI?@GR;3O#BC8:9MBI07]#476#EJ6>?@DC=@4505Bub<6707;#GR6#07BKO#BIa76#EF8jB >À´_gCW @ ´`d /1D!=@?LGRA7; 6#DI6#9<9<EFBI=@; A5EF;7O#47=@6 4707? A7;#DI?@EFBI^`^`?@^`BI;#076 O#BI67DI6#9<9<EFBI=L? =@N76 BC079<67EF?@]#BI8:=@6i=@;#0iBIDf=L?LGHA5;#ghO7?@07O#;k;7EFBI]#BC076i?@Ok470GH;#GR6#079<;iO#Bfb<;#EF^`? O#BC67DC6#9<9<EÀBC=@;7d ü?²O#6#058:BI9<îhO#B6#076#EJ]#BC?cDCBIª76#EJ?²N7?²4707I6#8:A7EF678L8:BI;#076V=@N769<BI6#076 =@;#079<;&O#6#DIDCI?@07BQ8:;#9<EF;#A7BI? O#6#DIDI? =@;#8:9<?@079<6 O#BQ6#DC679<9<EJBC=@?@g²?@07?@DC;7]#?@GH67079<6 ?@D =@?@8:;ñG?@]#076#9<BI=@;#g=@;70é450Ü9<6#EJGHBI076é=@N76Ü O#6#9<9<;§#C7¤IT< :C@áLad 6#b<BI07BI?@GR; DCÄI£:áT Lá_ÝI §#I7¤IT< LQ@ =@;#GR6 DI? O7BIb<b<6#EJ6#07^`? 9<EF? DI6 =@;78:9<?@059<B O#BC67DC6#9<9<EÀBC=@N76EF6#DI?@9<BIa76#g εQ ó ε − ε dT©6#DT=@?@8:;VO76#DW#XZY«g εQ cGH?@]7]#BC;#EF6VO#B ^j67EF;#d êd K6 yA7EJ6#8:6#079<64507?yO#6#b<;#EFGR?@^`BC;#076O#6#D=@?LGRA7;O#BIEF6#9<9<;#EJ6#g=@;#GRA7?@EF64707? 47DC9<67EFBI;#EF6A7;#DI?@EFBI^j^`?@^`BC;70566#DI6#9<9<EJBI=@?uBIDñ=@?LGHA7;6#DI6#9<9<EFBI=@;658L9<67EF07;8:B ?@=@=@;#A7A7BI? =@;70þ25476#8:9<? A5;#DC?@EJBC^`^`?@^`BC;#056#gO#?@07O7;þ;7EFBI]#BC056+?@Oþ470&0745;#a7; 9<6#EFGRBI076>076#DQDC?fO#6#078:BI9MîRO5Bu6#0767EF]#BI?fDCBQª#6#EF?@gPO#6#9<9<;ß<¤I Tá7#¤C< :I@á@d ôd ö?.A7EJ6#8:6#07^`?%O#BR4707?.O7BQ8:4707BIb<;#EFGRBI9Uîñ8:A7?@^_BI?@DC6O76#DHA7?@EF?@GR6#9<EF;O#C;7EFO#BI076 BC079<EJ;#O#47=@6>470345DC9M6#EJBC;#EJ6>9M6#EFGRBI076>6#076#EJ]#6#9<BQ=@;#guO#679M9<;á_L§#á7#¤CU :C@áLd Yd ©6#D²=@?L8:;®O#Bc=@?LGRA7B²?!ª7?@8:8:BI8j8:BIGR?(b<EJ6#27476#05^j?Lg²O7BCa76#059<?@07; BQGRA7;#EF9<?@079<B ?@07=@N76 B =@;#079<EFBIª#479<B¡?@8:8:;#=@BQ?@9<B ?@DIDII?@07BI8:;#9<EJ;#A#BI? O767DCDI?ÿ=@;#05O#47=LBCª7BIDIBC9<î 6#DC679<9<EFBI=L?@gK=@;#GR6>]#DQBT#ß<ß<T< K#¤QT< Lá#§# @CL d /\GH67=@=L?@07BC8jGRB«êg«ô 6 YO#BIa76#079<?@07;O#6#D«9<479<9<;9<EJ?@8:=@47EF?@ª#BQDIB«2747?@07O#;8:B459MBCDQBC^`^`?@07; =@?@GHA7B>6#DC679<9<EJBC=LBc?@DI9<6#EJ07?L9<Bc=@;#0(4707?!b<EJ6#27476#07^`?!8:47A76#EFBI;#EJ6®?@DIDI?!b<EF67274#6#07^`?!O5B EFBIDC?@8j8:?@GR6#079<;éO76#DIDC6Ü=@?@EFBQ=@N76é076#Ds=@EFBI8:9<?@DIDI;éDIBI2747BCO5;ñSU=@BIEF=@?.´`ï#ïì\^y076#DsWXZYZ[Ug6 ||. ⊥. ||. CAPITOLO 1. ⊥. 6.

(32) 8:47A76#EFBI;#EJ6®?@07=@N76 ?@DIDCIBI05a76#EF8:; O#6#Dc9<67GHA7; =@?@EF?@9<9<67EFBI8L9<BQ=@; O7BcEFBI;#EFBI6#079<?@^`BI;#076 O#6#DIDC63GR;#DI6#=@;#DI63O#6#DK056#GR?@9<BI=@;#gPDC?f=@47BP6#8:A7EF6#8:8jBI;#076> fO#?@9<?fO#?τ >À´_g | @ τ≈. SÊ´`d\~[. γ1 ε 0ε a E 2. O#;#a76 cBIDTa7?@DC;7EF6)O76#D=@?@GRA7;6#DC679<9UEJBI=@;#f g γ cBCDT=@;#67b<b<BC=@BI6#079<6VO7BTa7BI8:=@;#8jBC9<î ;#EFBI6#079<?@^`BI;#07?@DC6cO#Ba5;#DC47G6²6²a7?@DI6²ï#dC.ï ~ô°\D "UG > | g\(@½d©67DCDICBI079<6#EJa7?@DCDI;²O#67Ba7?@DI;#EJB O#6#B«=L?@GRA7B«67DC679<9<EFBI=LBO5?V07;#B«479<BIDCBI^_^`?@9<B«BI0y27476#8:9<;DI?@a7;#EJ;O#B«9<6#8:BIg N5?470a7?@DC;7EF6 8:47A76#EFBI;#EJ6?´`ïGR8:d©6#DIDCI?@GRª7BC9<;²O#BT25476#8:9<?>9<6#8:BIgo07;#B=@BA#;#EFEJ6#GR;Vτ 8:6#GRA7E6056#DCDI6 =@;#07O#BI^`BC;#07BoO#BoA7;#9<6#E

(33) 9<EF?@8:=@47EF?@EJ6²Bob<6#07;#GR6#07Boêgô#g Y²8L;#A7EF?3=@BI9<?@9<BCgo479<BQDCBI^`^`?L07O7;²470 =@?@GHA7; 6#DC679<9<EFBI=@; ;#8:=@BIDIDI?@079<6 ?b<EF6727476#07^`?8:47b<b<BI=@BC6#079<67GH6#059<6 ?@DC9M? SUGR;#DI9<; GH?@]7]#BC;#EJ6²O#B´`ïï²ìs^j[Ud°6#EF=@\B /@guBC0c27456#8:9<;²A7?@EF?@]#EF?@b<;#go=@BDIBIGRBI9MBC?@GR;²?ÛO#6#8:=LEJBCa767EF6 BCDP=@;#079<EFBIª#479<;>O#BI6#DQ6#9<9<EFBI=@;3?@DIDCQ6#076#EJ]#BC?h67DI6#9<9<EJBC=L?hO#67DK=@EFBQ8:9<?@DCDI;3DCBI2747BIO#;#d ö?hO76#078:BI9<îO7Bu6#0767EF]#BI?fDCBQª#6#EJ?ÛO5BC6#DI6#9<9<EFBQ=@?f >À´ @ [US 0 } XT[ SÊ´`d ´_ï[ ε S F ele = − 0 ε −ε 2. ||. ⊥. y07=@N76²BI0²27476#8:9<;²=@?@8:;#gBID8:6#]#05;²üZ`üo076#DoGH67GHª#EJ;²?3O#6#8:9<EJ?3BC0c6#2547?@^jBI;#0#6cSÊ´`d ´`ï[. O#6#EFBIa7?O#?LDIDCI?@a76#E3=@;#078:BIO76#EJ?@9<;ñBIDsDI?@a7;#EF;éb<?@9<9<;éO#?@Ds]#6#076#EJ?@9<;#EF6éA76#E>GR?@059<6#076#EJ6 ïg O#?@DIDC?cSÊ´`d ´`ï[ =@;#8:9<?@079<6O#BIb<b<6#EF6707^`?²O#BA7;#9<6#07^`BI?@DC 6 >ÄW @À(d XT8:8:6#07O#; Q 8:BO#6#O#45=@6é=@N76éDIC67076#EF]#BQ? òGBI07BCG?2747?@07O#;0Ü ò;#ε EJBI=6#07ε9<?@−9<;éε A7?@EF?@DIDC67DC?@G6#079<6éSU; ?@079<BCA7?@EJ?@DIDC6#DI?LGR6#079<6#[Z?@DK=@?@GRA7;#d 470727476#gKBIDuO#BIEF6#9<9<;7EF6>9<6#07O#63?@O>;#EFBI6#079<?@EF8:BKDC4507]#; DC?hO7BIEF6#^`BI;#076>O76#DP=@?@GRA7;36#DC679<9<EFBI=@;#d yDCDI?ÛSÊ´`d´jï[«=@;EJEFBI8:A7;#07O#6c4707?ÛO#6#078:BI9MîH8:A7?@^`BQ?@DC6cO7BKGR;#GH67079<;cO#Bub<;#EF^`?Û6#8:6#EJ=@BI9<?@9<; O#?@DK=@?@GRA7;>6#DI6#9<9<EJBI=@;>8:45DQDC6>GR;#DI67=@;#DI6#guO7?@9<?fO#? O[P[O:ó - Q«S 0 }.XT[ZS 0 × X[ SÊ´`d´´`[ ε ε τ _ 8:8L67EFa7BI?@GH; =@N76 BIDéGR;7O#47DI;O#6#DñGR;#GR6#079<; O7Bb<;7EF^`? A7EJ;#A7;EJ^`BC;#07?@DI6 ?@D 2747?@O#EF?@9<;>O#6#Do=@?@GRA7;#*d K6cBIDu=L?@GHA7; X ÛO#6#Du9MBCA5; XS` [Uó X-=@;#8:S ω [UgoBIDuGR;#G6#079<;cO#B b<;#EF^`?hN7?h4707IBC079<67078:BC9<î ||. τ ele = E 0 2 ε 0ε a cos β sin β cos 2 ωt = ε 0 ε a cos β sin β. 2. ⊥. 2. E0 E + 0 cos(2ωt ) 2 2. SÊ´`d½´_ê[. O#;#a76 β VDCI?@07]#;#DI;=@;#GHA7EJ6#8:;9<EF?yBIDO#BIEF6#9<9<;#EJ6Ü06BCD=@?LGRA7; Xd/pDGR;#GR67079<;O7B b<;#EF^`?- @gR2747BI07O#BCgDI?-8:;#GHGR?-O#B470.=@;#079<EJBCª7479<;;#8:=@BIDCDI?@079<66O#B470.=@;#059<EFBIª#479<; 8:9<?@9UBQ=@;#djK=@6#]7DCBI6#07O#;²;7A#A#;#EJ9<4707?@GR6#079<6²DI?3b<EF6#27476#07^j?3O76#D=@?@GRA7;#goA7;#8:8:BI?@GH;cbU?@EJ6 BC0ÜGR;#O#;é=@N76éBCDsA76#EFBI;#O;é?@8:8:;#=@BI?@9<;é?@D=@;#079<EJBCª7479<;é;#8:=@BIDIDC?@079<6éO#6#DsGH;5GH6#059U;éO#B b<;#EF^`?h8:BC?hGR;#DI9<;>GHBI07;#EJ6cO#6#BK9<6#GHA5BuO#BKEFBQ8:A7;#8:9<?h=@?@EF?@9<9<6#EJBC8:9MBI=LBuO#6#DKO#BIEF6#9<9<;7EJ6#guO7?@9<B O#?@DCDI?²SÊ´_Zd ~[Ud/Ä027456#8:9<6=@;#07O#BI^`BC;707BCgBIDO#BCEJ6#9<9<;#EF6V07;#0VEJBC678L=@6V?²8:6#]#47BIEF6VDC6VEF?@A7BIO#6 ;#8:=@BCDIDQ?@^jBI;#07BO#67DGH;#GR6#059<;O#Bb<;#EJ^`?6#O6#8j8: ; ¡`8j6#079<6 ¢²8L;7DC?LGR6#079<6BCD=@;7079<EFBIª#479<; 8:9<?@9UBQ=@;#£ d 450727476#g.470=@?@GRA7;;78L=@BIDQDC?@079<6 ?LO?@DC9<? b<EF6#27476707^j? O56#D.9<479<9<; 6#2747BIa7?@DC67079<6>?@O34703=L?@GRA5;>6#DC679<9UEJBI=@;>8L9<?@9MBI=@;>O7BPBI079<6#078:BI9<îA7?@EFBP?@DKa7?@DI;#EF¤6 !Kd. CAPITOLO 1. 7.

(34) öBI079<6#EJ6#8:8L?@059<6cb<?@EF6c4703=@;#05b<E;#079<;c9<EJ?ÛBoGR;#GR6#079<BuO#Bob<;#EJ^`?Û6#8j6#EF=@BI9<?L9<BoO7?@BK=@?@GHA5B GH?@]7076#9<BC=@;!6#O!6#DC659<9<EFBI=L;#¤d y A7?@EJBC9<î.O#B3GR;#GR6#079<;!6#8:6#EF=@BI9<?@9<;!8L45DÛ8LBQ8:9M6#GR?@g3DI? EF6#DI?@^`BC;#056>9<EF?fBKO#4763=@?LGA7BK ÛO5?@9<?hO7*? XóVì µ χ SÊ´`d´`ô[ 0. a. ε 0ε a. K;#8:9<BI9<476#07O#;#gc076#DIDC?!SÊ´`d´`ô[Ug²Bca7?@DC;#EJBCgcBC0NK/Äg²O#67DCDI6®?@07BI8:;#9<EJ;#A7BI6 O76#D²=@EFBI8:9<?@DCDQ; DCBI2747BIO#;W#XZY?9<67GRA76#EJ?L9<47EF??@GRª7BI6#079<6#g χQ ó´`dQô.Y ⋅ ´`ï x0¥ 6 εQ ó´´_g«8LB«9<EÀ;#a7?@g«?@O 6#8:6#GRA7BC;#g=@N76ñ470é=@?LGHA7;ñGR?@]#07679<BC=@;ñO#Ba dZ~ | ´`ï ¥ y 8¦U" G SUY(ó´`ïs[Ug=@N76ñ Ü?@D. DCBIGBC9<6O#67DIDI6A7;#8:8:BCª7BIDQBC9<îyO#B±EJ6#?@DIBI^`^j?@^_BI;#0768:A76#⋅EJBIGR6#079<?@DI6#g

(35) Ü6#2747BIa7?@DI6#079<6ñ?@O470 =@?@GHA7;.6#DC679<9<EFBQ=@;O#Bc´_dCï#We " µGRgRb<?@=@BIDIGH6#059<6.EF67?@DIBC^`^_?@ª#BQDC6.BI0.DI?Lª#;#EF?@9<;7EFBI;#d ?@D A747079<;>O#BKa7BC8:9<?hA7EJ?@9<BC=@;#gK2747BI07O#BIgu hGR;#DI9<;>A7ZB h8:67GA7DIBC=@6>A7EJ;#O#47EJEF6>?@DI9<BuGR;#GR6#079<BuO5B b<;#EF^`?hDC?@a5;#EF?@07O#;>=@;703Bu=L?@GRA7Bu67DI6#9<9<EJBC=LBId. om n § ¨

(36) t5t5

(37) v#z#xC}pVKVuwP{,+Pxpv>uxTv#wPz7rK{_v`++Kxpr /10!27476#8:9<;(A7?@EF?@]7EF?@b<; A#?@EFDI6#EF67GH;(O#6#DQDCI6#076#EJ]#BI?k?@8:8:;#=@BQ?@9<?k?@DIDCQBC079<67EF?@^_BC;#056 O#65D =@EFBI8:9<?@DIDI;DIBC2745BCO#;V=@;#0VDI68:47A76#EJb<BC=@B=@N76VDC;VO#6#DIBCGRBI9<?@07;#g=@N76A#;#8:8:;#07;V6#8:8:6#EF6V8:BC? 470²8:47ª#8:9<EF?@9<;²8L;7DCBIO#;#g=@;#GR6?@O6#8:67GRA7BI;DI68:47A76#EJb<BC=@BO#Ba76#9<EF;²O#BT4507?>=@6#DIDI?@g8:BI? DC?h8:47A76#EJb<BC=LBI6>DQBCª#67EF?fO#6#DP=@EJBI8L9<?LDIDI;>8L9<658L8:;>S½ \ _:ß<L@@C#u I@á@¬ © Ýá L@[Ud /1DKGR6#^`^j;>=@N763O#6#DCBQGRBC9M?hDQ?hb<?@8L6>056#GH?@9MBI=@?fBC059U67EF?L]#BI8:=@6>=@;#03DC;38L9<EJ?@9<;>O#BuGR;#DI6#=@;#DI6 8:47A76#EFb<BI=@BI?@DC6#g]76#076#EJ?@07O#;òO#6#B\GR;7GH67079<B\O7B\b<;#EJ^j?=@N76ò;#EFBI6#079<?@07;òBIDO#BIEF679<9<;#EJ6ÜBI0 4707?ò=@6#EF9<?òO7BIEF6#^`BI;#076#g

(38) O7?@05O#;ñDC47;7]#;ñ?@D

(39) b<6#07;#GR607;ñO76#DCDIÄ@á_L#Cá@ad 6#b<BI07BC?@GR; DCÄ@£j£:lß<@@I¤I=@;#GH6kDC?.O#BCEJ6#^`BC;7076lO#67DÛO7BCEJ6#9<9<;#EJ6k=@N76lGRBC05BCGBC^`^`?DQC670767EF]#BI?O#B BC079<67EF?@^`BC;70768:47A76#EJb<BC=@BQ?@DI67gHBI0?L8:8:6#07^`?-O#B=@?@GHA5BR6#8:9<6#EJ07BId X8L8:; %8:A767=@BCb<BI=@?L9<; O#?@DCDI?=@;7A7A7BC?VO#B«?@07]#;#DIB«S θ- g φ- [Ug«O#;#a76 θ- BI07O#BI=@?DIC?@07]#;7DC;A7;#DI?@EF6SUO#6#9<9<;?@07=@N76 ^j6707BC9<?@DI6#[±9<EJ?DIC?@8:8j6b<?@=@BCDI66DI?07;#EJGH?@DI6?@DIDICBI079M6#EJbU?@=@=@BI?@g«G6#079<EF6 φ- VDpI?@07]#;#DI; ?@^jBIG479<?@DC6þ9<EÀ? DII?@8:8:6þbM?@=@BIDI6þ6#Oþ470&?L8:8:6&O#BVEJBCb<6#EJBCGR6#079<;þ8:=@6#DI9<;þ8j47DVA7BI?@07; O#6#DIDCQBC059<6#EFb<?@=@=@BI?LdÜü? O#BQEF6#^`BI;#076O#67DCDIC?@8j8:6b<?@=@BQDI6O#BIA76#07O#68:BI? O#?@Dò=LEFBI8:9<?@DCDQ; DCBI2747BIO#;#gK8:BI?fO#?@DQDC?f8:;#8:9<?@05^`?h=@;#03=@45BKBIDK0767GH?@9MBI=@;3 hBC0Û=@;#079<?@9<9<;7d /103]76#076#EF?@DI6#gKA7;#8:8:BI?@GR;3O#BI8:9MBC07]7476#EF6>O#4563=@?@9<6#]#;#EJBC6>O7BK?@07=@;#EF?@]7]#FB ´`d §#_T_ L@g>2745?@07O#; 4707?!8:47A767EFb<BI=@BC6(?@GHGR6#9<9<6!A7\B lO#B>470!?@8:8:6 b<?@=@BIDC67g A76#EF=@N7Ù 6#8:BI8:9<;#07; O#BIa76#EF8:6 O#BIEF67^`BI;#07BÚ=@N56 GRBI07BIGRBI^`^`?@07; DIC67076#EF]7BC? 8:47A76#EFb<BI=@BI?@DC6 êd á_§#_T _LLgu2747?@07O7;>6#8:BC8:9M6>47034705BI=@;>?L8:8:63b<?L=@BCDI6#d BIb<6#EJ6#07O#;#=@Bk?@DCDI?³oBI]#45EF? ´_Zd Ygl=@;#078:BIO#6#EFBI?@GR; 470 8:BC8:9<6#GR?O#Bl=@;#;7EFO#BI07?@9<6 =@?@EF9<6#8:BQ?@076#go=@;70>BIDuA7BI?@07) ; T V38:47DIDIIBI079<6#EFb<?@=@=@BQ?Û9<EF?hBIDoXZü©.6>BCDu8:45ª#8:9<EF?@9<;7go6>DIC?@8j8j6 à478:=L6#059U63O#?LDK8:47ª#8:9<EJ?@9U;5d K6lBIDh8:47ª#8:9<EF?@9<;k=@N76lO76#DCBIGBC9<?BQDhXZ¨ BC8:;#9<EJ;#A7;#gÛ07;70l=@I ?@DC=@4507?O#BQEF6#^`BI;#076 A7EFBIa7BIDC6#]7BC?@9<?kO7BÛ?@DCDQBC0767?LGH6#059<;(076#D3A5BC?@07w ; T V5d3XZI @g32747BI07O#BIgÛ4707?k8jBIGRG6#9<EFBI?kO7B EF;#9<?@^`BI;#076 ?@9<9<;#EF07; ?@DIDIC?@8:8:6àÚ6 8jBkA5?@EFDI?O#B!§#_T _L@à_Iá_ @à`Q²¦7 @¤C:d öI6#076#EJ]#BC?cO#B8L45A76#EFb<BI=@BI67g O7B =@45B A7?@EJDC67EF6#GR;9<EJ?²A7;#=@;#gO#BIA76#07O#67EFî38:;#DI?@GH67079<6O#? -<du°o;#8j8:BC?LGR;>O#BQ8:9UBI07]#456#EJ6>BP8L67]#476#079<BP9<BCA7BPO#BK?@07=L;7EF?@]#]#BI; θ á#R#áT Lá`ÝoC@á@g 2747?@05O#;yDIC?@8:8:6b<?@=LBCDI6 ;#EJ9<;#];#05?@DC6?@DCDI?²BI079<6#EFb<?@=@=@BQ?S θ-uó • ïõF[Ê#BI0327476#8:9<;>=@?@8:;3DCI?@05=@;#EJ?@]#]#BI;> h07;#03O#6#]#67076#EF6 CAPITOLO 1. 8.

(40) •. •. Ý¤CoL@g2747?@07O#;V]#DIB ?@8:8jBb<?@=@BIDIB]#BI?@=@=LBI;#07;V8:47D A5BI?@07;VO#B8L67A7?@EF?@^_BC;7076S θó ~ïõJ[Ê\BI0ñ27476#8:9<;=@?@8:;DIC?@07=@;7EF?@]#]#BI; ÜO#6#]#6#0767EF668:B±N7?@0705;-BI07b<BI07BI9<B v ?@8:8:BTb<?@=@BIDIBIgT=LBC;# c9<459U9<6DC6²;#EFBI6#079<?@^`BC;707B056#DA5BC?@07;V8:;#07;V6#0767E]#6#9<BI=@?@GR6#079<6 6#2747BIa7?@DC67079<B @á_I@ák; C¤ u á@g32747?@05O#;!]#DIB3?@8:8jB>b<?@=LBIDQB3N7?@0707;(DII?@07]#;#DI;(^`6#07BI9<?@DI6 θO#BCa56#EF8:;²O#?3ï#õ±6 ~ï#õL8:BO76#b<BC07BI8:=@6c?@07]#;#DI;²O#BÝ7LT C¤ θª DII?@05]#;#DC;cbU;#EFGR?@9<; O#?@DCDIQ?@8:8L63b<?@=LBIDI63=@;#03BCDPA7BC?@05;>O#6#DIDI?f8:47A76#EJb<BC=@BI63632747BI07O#0B θª ó π − θ-5d 2. z>0: CLN z<0: substrato. µ:¶ · ¸¹<º

(41) »½¼ «¾i#Ç Ø7ÅË ÁÍ3m5È\É ÈUÏCÁ Ç ÁÄÂJÍJÅ Ç7ÅË1Î«ÉUÁ ÓFÈÆÀÁÄÅUÇ7ÈÉ ÈË Ë¬ ÎFÂJÂÀÈoÏ ÎFÍMÁ Ë1È\È\ÉÊÈ ËÉUÁ ÓÈÊÐCÐIÅÓFÈFkPÎMË Ë¬ Á Ç7ÐIÈÓ<Ï½ÎJÍFÍMÁÄÎ Ð ÓÎZÒ<ÇR ú ®¯È ÉÒUÇRÂ½Ò o ÂÀÐ ÓÎFÐIÅ_7Ô ®°¬ Á Ç5ÐIÈ Ó<Ï ÎFÍJÍMÁÄÎÂÄÁÐ ÓFÅ5Ö Î«Â½ÒË`Ã Á1ÎMÇ7jÅ ± nL¼ K6#g\BI07a76#=@67g\BCD8L45ª#8:9<EF?@9M;ò?=@;#079<?@9<9<;Ü=@;#0òBID\076#GR?@9<BI=@;ò ?@05BC8:;#9<EJ;#A#;#g\=5;7GH6ò?@O 6#8:6#GRA7BC;y470y=@EJBC8:9<?@DQDC;y;4705?V8:47A76#EJbUBI=@BI68:9<EF458L=LBQ?@9<?VBI0y4707?=@6#EF9<?O#BCEJ6#^_BI;#056#gZ]#DCB ?@07=@;#EF?@]7]#BoA7DI?@07?@EJ6>6>=@;07BI=@;>A7;#8:8:;#0#;>6#8:8:6#EJ6>0#;#03O#6#]76#076#EFBIdu/Ä0>27456#8:9<;²=@?@8:;>8jB A7?@EFDI?@guEJBC8:A76#9<9<BIa7?LGR6#079<6#gO#Bu?@07=@;7EF?@]#]#BI;á#Rá_T_o#áh6>O#BK?@05=@;#EF?@]#]#BI;á#è#¤II¥¦ á@d %0i=@?@8:;kA5?@EF9<BI=@;#DC?@EJGH65079<6kBIGHA7;7EF9<?@079<6#gfA76#EJ=@N7Ù?@GRA7BI?@GR6#079<6i479MBCDQBI^j^`?@9M;k056#DCDI6 ?@A7A7DIBC=@?@^`BI;#07BTO76#BT=@EJBI8:9<?@DIDIBDIBC2547BCO#BQg >27476#DIDC;²BC0²=@47BBIDT8:47ª78L9<EJ?@9<;;#EJBC6#059<?@079<6a7BI6#076 EF6#?@DIBC^`^_?@9<;O#67A7;#076#07O7;4#0V8:;#9<9<BIDI68:9<EF?@9<;O7B G?@9<67EJBC?@DI6A7;#DIBIGH67EFBQ=@;#g O7B 8:A7658L8:;#EJ6 BC07b<67EFBI;#EF6¢?´`ïï 07GRg8:47DIDI?þ8L45A76#EFb<BI=@BC6¡O#B470¡a56#9<EFBI07;#d/1DA7;#DIBIGH6#EJ;¢a7BI6#076 8:47=@=@678:8:BIa7?@GR6#079<68:9<EF458:=@BI?@9<;=@;#0470A7?@0707; O7B-a76#DCDI479<;DC4705]#;4707? O#?@9<? O#BCEJ6#^`BC;7076#°d KB a76#EJBCb<BI=@?8jA76#EJBCGR6#079<?@DIGR6#079<' 6 >½´`W#g ´ | @=@N76BIDZO7BIEF6#9<9<;#EJ68:B O7BI8LA5;#076 076#DA7BI?@07;=@;079<6#076#079<6DCC?@8:8:6O7B8:9<EF478:=LBI?@GR67079<;ò6DI?07;EJGR?@DC6?@DCDI?8:47A@6#EFb<BI=@BC67g =@;#0 470 ?@07]#;#DI; O#B&A7EJ6#9<BCDI9 0745DCDI; ; O#B&A7;#=@N7B&]#EF?@O7BþS<EFBI8LA56#9<9<BCa7?@GR6#079<67g ;#EFBI6#079<?@GR6#079<;y;#GH;7]#6#076;y;O#67ª#;#DIGH6#059<69<BQDC9<?@9<;#[UdZüC?@05=@;7EF?@]#]#BI;=@N56076yO#6#EFBIa7? 8:?@EFîDCI;#]#]#679U9<;3O#BK2747678L9M?h9<6#8jBId öI?@07=@;#EJ?@]#]#BC;A74 /Ú6#8:8j6#EF6O#6#8:=@EJBI9<9<;9<EJ?@GRBI9<64707? b<4707^`BI;#07³ 6 ²«S 0 Ć[Ug-O#6#9<9<? ß¦à`Cá_o§7

(42) __JTIÜ§#@á_:#TCáLg

(43) O;#a56%.0 ´± òBCDO#BIEF6#9<9<;#EJ6ñ8L45DCDI?Ü8j45A767EFb<BI=@BC6#d \?@DC6Vb<4707^`BC;7076678:A7EJBCGR6VBIDDI?@a7;#EJ;#gA76#E4707BC9<îÛO7B?@EJ6#?@g076#=@678:8j?@EFBI;?c8:A7;#8:9<?@EJ6BQD O#BCEJ6#9<9<;#EJ6+O7?@DCDI?®A7;#8:BC^`BI;#076þO#BV6#2747BIDCBIª#EFBI;þ8:9<?@ª#BIDQ6¡.0 -òSU?@8:8:6þb<?@=@BCDI6#[Ü?®27476#DIDC? BC07O7BC=L?@9<?fO#?Û.0 Ćd ö6.O7BIEF67^jBI;#07BO#6#DIDII?@8j8:6%b<?@=@BCDI6%6.O76#DO7BIEF6#9<9<;#EJ6%BI0%8L45A76#EFb<BI=@BI6%8L;707;.6#8:A7EF678:8L67g EFBI8:A76#9<9<BCa5?@GH6#059<6#gO#?@DQDC6=@;#A7A7BI6òO#B\?@07]#;#DIB\^`6#07BI9M?LDC6ò6?@^jBQGR479<?@DC6S θ-<g φ-[6òS θ µ g CAPITOLO 1. 9.

(44) [\Sa76#O#6#EJ6³uBC]#45EF?²SÊ´`d\Y[U[Ud°o6#E=@;7GH6V?@ª#ª#BI?LGH;O#6#b<BI07BC9<;VDC?²b<4705^jBI;#076t²«g EJBI8L45DC9<? =@N76 SÊ´`d´#Y[ ²«S ó -Mg ó -U[ZóVï θ µ θ φµ φ öA7;#8:8:BIª#BIDC6>EJ67?@DCBI^_^`?@EF63O#6#DIDI6>=@;#07b<BC]747EF?@^`BI;#07BuBI0Û=@47BKBIDKO7BCEJ6#9<9<;#EF6>8:BKO7BI8:=@;78L9<BKO7?@DIDC? A7;#8:BC^`BI;#076+O#B6#2747BIDIBIª#EFBQ;#ga7?@EFBI?@07O#;+8:;#DI;+4707;¡O#6#BO#476þ?@07]#;#DIB ; d yO 6#8:6#GRA7BC;#g«4707?y=@;#07b<BI]#47EJ?@^`BC;#076BI0=@47Ba7?@EJBC?8:;#DI; φµ S θ µ GH?@059U670747θ9<µ ;47]#φ47µ ?@DI6? -<[

(45) VEJ6#?LDCBI^`^`?@9<?²EF?@=@=@N7BI45O#6#07O7;BIDZ056#GH?@9MBI=@;9<EJ?²O#476y8:45ª#8:9<EF?@9MBZA7BI?@07B 6yA7?@EJ?@DCDI6#DQB θ =@N76>BC05O#47=@?@07;>4703?@07=@;EF?@]#]#BI;>;#GR;]#6#056#;#guGR?hDI4#07]#;cO#BIEF6#^`BI;#07BK07;#0>A7?@EJ?@DCDI6#DI6#du/Ä0 27476#8:9<;=@?@8:;?@ª#ª#BI?LGH;4707?V]#6#;#GR6#9<EFBI?O#B«A547EF;K c«I£PJ BCD«O#BIEF679<9<;#EF6O#6#DZXZö©(N7? EF;#9<?@^`BI;#07B8:;7DC;²O7B9<BIA#;²?5^`BCGR479M?@DI6#goA76#E±=@47Bo8:;#DI;²DC6²a7?@EFBI?@^`BC;#05BO#GB ²EFBI8:A769<9<;²? φµ 8:;#07;lBIGRA7;#EF9<?@079<BIdhöI6#056#EJ]#BI?O#Bf?@07=@;#EJ?@]#]#BC¶ ; ²«S g [VO#BIa76#079<?@gh2747BI07O#BIgh4707? b<4707^`BC;#056O#6#D«8L;7DC;?@0#]#;DI;?@^jBIGR479<?LDC6 φµ 6a7BC6#056θO#µ 679<9<φ?µ __JTIy§#@á_:#TIá @àjIc¦7 @¤C ²(Q3·<S [«' ó ²«S θ-<g φµ [ SÊ´`d´`W[ φµ K47DIDC?>8:47A56#EFb<BI=@BC6²BIDO#BIEF6#9M9<;#EJ6EFBI8:6#079<6O#B470²GR;#G6#079<;O7BTb<;#EJ^`?>?@^jBIGR479<?@DC65gTBIDT=@4@B GH;7O#47DC;>A56#E4707BI9<îRO5BK?@EF65?Û » ∂ ¹3º S´`d ´ | [ τ¹ = − φµ. ∂φ¸. 74 6#8:9<; GH;7GH6#059U; O#B²b<;#EF^`?(9<6#07O#6 ?@O ?@DCDIBC056#?LEF6 BIDO#BIEF6#9<9<;#EJ6&a56#EF8:;þDI? 8:47? A7;#8:BC^`BI;#076>O#BP6#2747BIDCBQª#EJBC;3SU?@8:8:6>b<?@=LBIDC6#[Ud °6#E®A7BI=@=@;#DIBñ8LA5;#8:9<?@GH67059<B-O7?@DIDI?ÚA7;#8:BI^_BC;#056O#BñGRBC05BIGR?6#0767EF]#BI?@gA7;#8:8:BI?@GR; 8:a7BCDI47A7A7?@EJ¼ 6 ²(Q3·?@Dh8:6#=L;#07O7;!;#EJO#BC056l?@9<9<;#EF07;l?@DIDC?A7;#8:BC^`BI;#076lO7Bh6#2747BIDIBQª#EFBI;l6#g 9<6#076#07O#;>=@;7079<;>O#6#DIDC?hSÊ´_d #´ Y[Ugu8:BK;#9<9<BI6#056 SÊ´`d#´ [ 1∂ W Waz (φ s ) =. 2. 2 ∂φ s. az 2. 47BC05O#BIgKBIDPGH;7O#47DI;>O#6#DKG;#GR6#079<;>O#BKb<;#EF^`?h . φ s = φ0. τ¾ = −. ∂2. Á. ∂φ ½. ¾l¿ 2. À. (φ½. (φ s − φ 0 )2. − φ0 ). SÊ´`d´[. φ = φ0. BCDòGR;#GR6#079<;ÚO#BÜb<;#EJ^j? O7;#a7479<;Ú?@DIDIC?@07=@;7EF?@]#]#BI;Ú9<6#07O76Ú?¢EJBCA7;#EJ9<?@EF6DII?@07]#;#DI; ?@^jBIG479<?@DC6a76#EF8:; φÂ Ãd PBhO76#b<BC07BI8:=@6BIDÛ@á##ß<ß<I@C \ §#H__FC.§7fLá L#TIá @àjIc¦7 @¤CW ²Q SÊ´`d#´ ~[ ∂ W Wa =. 2. az. ∂φ s 2. θ s = θ 0 , φs = φ 0. y07=@;#EF?l;#]]#BIgc07;#0( l07;#9<;®2547?@DC6 8:BI?lDI?lb<;#EJGH?lO#6#DQDC?lb<4707^`BC;#056 ?@07=@;7EF?@]#]#BI; ?@^jBIG479<?@DC6Ä²(Q3Ü · A76#EBO#BCa56#EF8:B8:47ª78L9<EJ?@9MBy2747?@0@O#;+S ´ -U[é07;#0þ A#BI=@=@;#DC;#d. \479<9<?@a7BI?@gA76#EcBID=@?@8:;ñA5?@EF9<BI=@;#DI?@EF6ñO7B?@05=@;#EF?@]#]#BI;ñA747φEJ?@GH− 6#φ059<6?@^`BQGH459<?@DI6é8:Bb<? =@;#GR47076#GR6#079<6¡478:;¡O#67DQDC?&b<;#EJGH45DC?&b<6#07;7GH6#05;#DC;#]7BC=@?&A7EJ;A7;#8:9<?&O#Å ? T?LA7BC07By6 °?@A7;747DC?@E >J#Zg ~(@# CAPITOLO 1. 10.

(46) Waz (φ s ) =. 1 WRP sin 2 (φ s − φ 0 ) 2. SÊ´`dIêï[. /103GR;#O#;3?@07?@DC;#]7;#gu8:BKO#6#b<BI07BC8:=L6>DI1 _FCh§7K@á L#Cá>à`_ @¤Ih=@;#07076#8:8:?h=@;#0 DC?h8:;#DI?fEF;#9<?@^`BI;#076>O76#DIDCQ?L07]#;#DI;>^`6#07BI9<?@DC6 θµ d °6#EA7BI=@=@;#DI6EF;#9<?@^`BI;#07BEFBQ8:A76#9<9<;?@DIDIC?@8j8:6b<?@=LBIDC67gDQ?²SÊ´`dIêï[\ ²ª#6#0VO76#8:=@EFBI9<9M?²O#?@DIDI? ?@A7A7E;78L8:BIGR?@^`BI;#076>A7?@EJ?@ª7;#DIBC=@*? SÊ´`dIê´j[ 1 2 W (φ ) = W (φ − φ ) az. s. 2. RP. s. 0. 470727476#g²(ÆÇc=@;#BI07=@BIO#6Ü=@;#0éBID=@;76#b<b<BC=@BQ6#079<6éO7Bs?@07=@;7EF?@]#]#BI;é?@^`BCGR479<?LDC6ÜO#67b<BC07BI9<; 8:;#A7EF?@dGy 07;78L9<EJ?=@;#0#;#8L=@6707^`?@gfDI6k4707BQ=@N76iGHBI8j47EF6iO#Bh67076#EF]7BC?O7Bf?@07=L;7EF?@]#]#BI; ?@^jBIG479<?@DC6 6#8j6#]#47BI9<60567DCDICBI079<6#EJa7?@DIDC; O#Bñ?@07]#;#DIBO#?ïõ®?È#~ ïõ®8L;707;27456#DCDI6 6#b<b<6#9<9<47?@9<6cO#?@Du07;#8:9<EF;>]EF47A7A7;#goA767E

(47) 8:47ª#8:9<EF?@9<BuO#BK B _ 6#a7?@A7;EJ?@9<;c? | ïõ½> ´jï#¬´`êÀ@ g A76#EV8:47ª#8:9<EJ?@9<BO#B±XZêÉÀ> ´_ô(c@ 6%A76#EV8:47ª#8:9<EJ?@9MBO#B

(48) A7;#DIBCGR6#EFBb<;#9<;#8:6#078:BIª#BQDCB½> ´#Y(½@ d/. EFBI8:47DC9<?@9MBR8:A76#EFBQGR6#079<?@DQBRO#BIGR;#8:9<EF?@07;=@N56#gHA56#E2747678L9<BGR?@9<6#EJBI?@DIBIgRDI?%b<;7EFGR47DC?-O7B ?@A7BI07BI¬K°o?@A7;#47DI?@E SÊ´`dCêï[ O76#8:=@EFBIa76 ª76#076 DII?@07O#?@GR6#079<; O#67DCDQC67076#EF]#BI? O5B ?@07=@;#EF?@]7]#BC;+?@^`BIGH479<?@DI6#gV?@07=@N76¡A76#E]7EF?@07O#B?@07]#;#DIBCg?@Dy=@;#079<EJ?@EFBI;¡O#By2547?@079<; ?@a7a7BI6#076>A76#EDII?@07=@;#EF?@]7]#BC;>^`6#07BI9<?LDIW 6 >À ´ g #´ (@½d öIBC059<6#EFb<?@=@=LBI?ÛBC07a7678L9MBI]#?@9M?ÛBI0>27476#8:9<?Û9<6#8:Bo Û25476#DCDQ?Û9<EF?ÛBIDo=@EJBC8:9M?@DIDC;>DCBI2747BIO#;>WXZYé6 470þ8:;#9<9<BCDI6+8:9<EF?@9<;+O#BA#;#DIBCGR6#EJ;¡S<DC?lÝTá#\¤ VIHI§#L[é8:9<EF458L=@BI?@9<?@d 47678:9<;+9<BCA7;+O#B BC079<67EFb<?@=@=@BI?3 Û25476#DCDI;c479<BIDIBI^`^`?@9<;cA76#E

(49) DI6c?@A7A7DIBC=@?@^`BI;#07Bu6#DC679<9<EF;#¬P;#9<9<BC=@N56cO#6#Bu=@EFBI8L9<?@DID B DCBI2747BIO#BIdu°o6#E

(50) 9M?@DI6>BC079<67EFb<?L=@=@BI?ÛDIQ?@07=@;#EF?@]#]7BC;c?@^`BIGR479<?@DI6> Ûb<;#EJ9<6#do/Ä0>9<?LDIBu=@;707O7BC^`BI;#07BIg DC6.EJ;#9<?@^`BC;707BO76#DO7BIEF6#9<9M;#EJ6.BI0%8:47A76#EFb<BI=@BI6%A7EF;#O#;#9<9<6.O#?@B=@?@GRA7B?@A7A7DIBC=@?L9<B8:;#07; A7BC=@=@;7DC667gA76#EJ=@ZB /@g0767D8:6#]#47BI9<;479<BIDIBI^`^j67EF67GR;8j6#GRA7EF6DI?-8j6#GRA7DCBQ=@6EJ6#DI?@^`BI;#076 SÊ´`dCê´j[lA76#E O#6#8:=@EFBIa76#EJ6 DII?@07=@;#EF?@]#]7BC;#d-©;#07;#8:9U?@079<6DC?Ú]#EF?@07O76BIGRA7;EF9<?@07^`? ?@A7A7DIBC=@?@9<BIa7?ÛO#Bo25476#8:9<?ÛBC059<67EFb<?@=@=@BI?@go?LDuGH;#GR6#079<;c05;#0c6#8:BI8L9<;707;cGHBI8:47EJ6cO#6#DIDC?Û8:47? 6#076#EJ]#BC?ÜO#B?@07=@;#EF?@]#]7BC;?@^`BQGH479<?LDI6#g

(51) GR?ò8:?@A7A7BI?@GR;8:;#DI;=@N76BID

(52) =@;#6#b<b<BI=LBC6#079<6O5B ?@07=@;#EF?@]7]#BCÈ ; ²Q3 éGR?@]#]#BI;#EF6-O7B3´`ï x0ÊÃË "U!G 1düC?L8:8:6#07^`?éO7B±O#?@9MB8:A76#EJBCG6#079<?@DIB O#;#a7479<?@g=@;#GR6a76#O#EJ6#GR;#gR?@Db<?@9<9<;=@N76DI6;#EJO#BC07?@EFBI69<6#=@07BI=@N76A767EyDI?-GHBI8:47EJ? O#6#DIDCI?@07=@;#EJ?@]#]#BI;%?@^jBIGR479M?@DC6%O76#8:=@EFBQ9<9<6%BC0-DI6#9<9<6#EJ?@9<47EF?ñ07;#0%8:;#05;.?@A#A7DIBC=@?@ª#BIDQB?LO ?@07=@;#EF?@]7]#B(=@;#8:ý!b<;#EF9<BId!X«;7GH6 a56#O#EF6#GR;#g!BC0@a76#=@6#g!B(G6#9<;#O#B!8:A76#EFBQGR6#079<?@DIB 8:a7BCDI47A7A7?@9<B0767D07;#8:9<E;DC?@ª#;#EF?@9<;7EFBI;ÜA767EFGR6#9<9<;#07;òDC?yGRBC8:47EJ?O#B?@07=@;7EF?@]#]#BGR;#DI9<; b<;#EF9<BId mon ã. qsv#}pz#ru}Cr%PK}

(53) z#v# r%Kxp{Êu||UrK{Ê%xÄwW{ Kt@Kw.@véPx±Pw-z7v# Pr%>v+KwP|xpz7r xÄw +KPrK3u|U{ xpvcKx7| Ìfxpt5| /10k27476#8:9<;!A7?@EF?@]#EJ?@bU;!O#6#9<6#EFGRBI076#EF6#GR;lBCDh=@?@GRA5;!O7BCEJ6#9<9<;#EF6lO#BÛ4707;l8L9<EF?@9<;!O7B XZö©g3A7;78:9U;!9<EF?kO#476!8:47ª#8:9<EF?@9<B3A7BI?@07B3A7?@EF?@DIDI6#DIBÛ6!8:;#9<9<;A7;#8:9<;(?@O(450(=@?@GRA7; GH?@]7076#9<BC=@;7dH/Ä02747678:9<?-=@;707b<BC]747EF?@^`BC;7076BIDHO#BIEF679M9<;#EF6N5?%4707?%O#6#b<;#EJGH?@^`BQ;#076O7B A747EF;ÜK cZC£P d mon ã npm qsv#t5ryPxt5|{_v7|rt@P3xÍxCw

(54) xpwuxp|Ur XZ;#078:BCO76#EFBI?LGH;%DI?ñ=@;#07b<BC]#47EJ?@^jBI;#076%O#B³uBC]#47EJ?ñS ´jdIW[Ud°T;#07BI?@GR;%DC?ñ8:47A767EFbUBI=@BC6%O5B 8:6#A7?@EF?@^`BI;#0760767D A7BI?@07;àHóïy6VBID076#G?@9<BI=@;V076#DQDC?²EJ6#]#BI;#076à ï(d yA7A7DIBI=@N7BC?@GR; CAPITOLO 1. 11.

(55) 470&=@?@GHA7;þGR?@]#076#9<BI=@;+ì DC4507]#;þDCI?@8j8:6ÎT7dXZN7BI?@GBC?LGR; DIQ?@07]#;#DI;þbU;#EFGR?@9<; O#?@DCDIQ?@8:8L6yb<?@=LBCDI6=@;70yBIDZ=@?@GHA7;y6 φµ DII?@07];#DI;b<;EJGR?@9U;yO#?@DZO#βBIEF6#9<9<;7EF6=@;70yDIC?@8:8:6 T7d. z. µ:¶ · ¸¹<º» ¼ Ï#¾iÇ7É ÎMÌ

(56) ÈUÇ7ÐIÅòÉ ÈUË3ÉÁ ÓFÈÊÐCÐIÅÓÈÜÉUÁ3Ò<ÇÍFÎMÌ Ã ÁÄÅUÇ7ÈòÉÁ3ú ®¯¢ÍFÅUÇÒ<Ç7ÎÂJÒ<Ã5È Ó<ÏIÁ1ÍMÁÄÈÜÍFÅUÇ ÎMÇ7ÍFÅÓÎMØ Ø_ÁÄÅ Ã Ë1Î1Ç7ÎMÓ0È k5Á ÇsÃ_ÓÈ ÂÀÈUÇ Æ`Î\É ÁuÒ<ÇÛÍJÎMÌ Ã7ÅÌ

(57) ÎMØ Ç7ÈÊÐ ÁÄÍFÅÑÐk@Ã7ÎMÓÎMË Ë1ÈË1Å

(58) Î1Ë Ë¬ ÎFÂJÂÀÈ°±ÔÕ ËoÂÀÈ ØÊÌ

(59) ÈÇ5ÐIÅ Ð ÓÎJÐCÐIÈUØ_Ø Á1ÎJÐCÅ ÂJÒUËPÃ Á1ÎMÇ5ÅsÆ Ò!ÓÁ Ç5É ÁÄÍFÎË ¬ ÎFÂÀÂJÈsÏ ÎÍMÁ Ë1ÈHÂJÒUË Ë¬Á Ç5ÐCÈÓ<Ï½ÎJÍFÍ1Á1ÎÂÀÒ,o ÂJÐ ÓÎFÐIÅÔÄÇ5ÈÌ

(60) ÎJÐ Á1ÍFÅ0k Ì±ÈUÇ5Ð ÓÈ«ÁTÂÀÈØ (Ì- ÈU-Ç7-Ð Á#) Á ÇÛÐ ÓÎJÐIÐpÅ±ÍFÅÇ7Ð Á Ç5Ò Å ÕZÖ{Ö{×PÁ Ç5ÉUÁ1ÍFÎ1Ç#Å«Ë1ÎÉÁ ÓFÈÆ½ÁÄÅÇ5ÈÉ È ËoÉ Á ÓFÈÊÐIÐpÅÓFÈ_Ô β Ø Ë ¬ ÎMÇ Ø7Å ËÄÅ Ð ÓÎ\Ë ¬ ÎFÂJÂÀÈ

(61) Ï½ÎJÍMÁ ËÄÈhÈ É

(62) Á ËÍFÎ1ÌZÃ5Å±Ì

(63) ÎMØÊÇ7ÈÊÐ Á1ÍF0Å k Ë1ÎRÉ_È5ÖIÁÄÎMÆÀÁÄÅÇ5ÈhÉ ÈËÉÁ ÓFÈÊÐIÐpÅÓFÈhÂJÒUË Ë1ÎÂJÒ<Ã7ÈÓ<ÏCÁÄÍMÁÄÈ É_Î1Ë Ë ¬ ÎFÂJÂÀÈÏ ÎFÍMÁ Ë1ÈÈ φÕQEÆ × Ø Ë ¬ ÎÄÇ_Ø5ÅË1ÅÐ ÓÎKÁ ËÉÁ ÓÊÈÊÐIδφÐCÅÓFÙ(È\Ø ÈoË ¬ ÎFÂJÂÀÚÈ ± kPÍFÅUÇ φÙ Ò φ ÕQeÆ ÒaÓ ×C¼ K6(ì ?@ª7ª#?L8:9U?@05^j?BC079<67078:;#gÛBCDÛ076#GR?@9MBI=@;!8:Bh?@DIDCBI076#?DI4707]#;lBCDÛ=@?@GRA7;l076#DIDC? EF6#]#BI;#076=@6#079<EJ?@DC6O#6#D=@?@GRA7BI;#0766A7;#8:8:BI?@GH;=@;#078:BIO#6#EJ?@EF6BCD=@?LGRA7BI;#0768:6#GRBI¬ BC07b<BI07BI9<;#du/Ä07b<?@9<9<BIgKDI?fA7EF6#8:6#05^j?hO#67DIDI?f8L67=@;#07O#?f8:47A76#EJb<BC=@BI6>S½à ÛH§@[Z07;#03BI07b<DC456#07^`?ÛBI0 GH;7O#;?@A#A7EJ6#^`^j?@ª#BIDI6DCI?L07O#?@GR6#079<;O76#DRO7BCEJ6#9<9<;#EF6.076#DCDI?-EJ6#]#BC;7076 ï ( à S§ "êd 470727476#gÛA767Eé2745?@079<;!EFBC]#45?@EFO#?i25476#8:9<?iEF67]#BC;7076#gÛ9<479<9<;!?@a7a5BC6#076l=@;#GR6l8:6lDC? 8:6#=@;#07O#?Ü8:47A76#EJb<BC=@BI6ñ07;#0ñb<;#8:8:6A7EF6#8:67079<66BCD

(64) =@?@GRA7BI;#076b<;#8:8:6BI07b<BC07BI9M?@GR6#079<6 6#8:9<6#8:; S½à → ∞[Ud>°o\B !a7BI=@BC05; ?@DIDC?k8:47A76#EJb<BC=@BI6 àóþï#g>=@B>8:?@EFî4707?k^j;#07?lO7B 9<EF?@078:BI^jBI;#0767gBI0¡=@47BDI6¡GR;#DC67=@;#DC67gA747EiEFBIGH?@056#07O#; 076#DA7BI?@07Ü ; T V@gEF47;#9<?@07; a7?@EFBI?@07O#;>DIC?@07]7;#DC;3?@^jBQGR459<?@DC6 φ S½àÊ[Udu/ÄDuO7BCEJ6#9<9<;#EF63EJBC8:47DI9<? SÊ´`dCêê[ 03óVSU=@;#8 φS½à [ZgK8:BC0 φS½à [Uguï#[ K47DIDC?8:47A76#EJb<BC=@BI6éS½àó.ï[H=@I 4707?=@;#GHA56#9<BC^`BI;#076é9<EF?DCI6#b<b<6#9<9<;éO#Ba7;#DI4#GH67g=@N76 9<6#07O#6®?@O®?@DIDIBC0765?@EF6®BIDcO7BCEJ6#9<9<;#EF6®076#DIDI?(O7BIEF6#^`BI;7076®BC0 =@47Bc8:;#07;®;#EJBC67079<?@9<6 DI6 GH;7DC6#=@;#DI6?@DIDICBI079<6#EJ07;yO#67D =@?LGRA7BI;#076ySU=@BI;# A5?@EF?@DIDI6#DI?@GR6#079<6?@D=@?@GRA7;#[Ug 6274767DCDI; O#6#DIDCI?@07=@;#EJ?@]#]#BI;#g=@N76 9<6#07O#6 ?@O ?@DCDQBI076#?@EF6 BQD²O#BIEF6#9<9<;#EJ6 DC4707]7;&DII?@8:8L6®b<?@=@BIDC67d yDCDII6#2747BIDCBIª#EFBI;#gBCDO#BIEF679U9<;5EF6VBI08:47A76#EJb<BC=@BI6b<;#EJGH?@gTEJBC8:A76#9<9<;?@DCDII?@8:8j 6 T5g450²?@07]#;#DI; Û ¬ s g 7 O # ; 7 a # 6 s g 7 A # 6 3 E @ = # ; 7 0 7 a # 6 7 0 I B # 6 7 0 ` ^ @ ? s g @ ? # ª 7 ª C B L ? G Ü ; 7 4 < 9 C B I D I B j ^ _ ^ @ ? < 9 Ü ; C B \ D : 8 I B GRª#;#DI; δφµ A767E φµ β δφ µ BC07O7BC=L?@EJ6DI;ñ8:A7;#8:9<?@G6#079<;ñO#6#D

(65) O5BCEJ6#9<9<;#EF6ñO#?@DIDQC?@8j8:6ñb<?@=LBCDI6#gGBI8L45EF?@9<;ñ076#Da767EF8:; ;#EF?@EJBC;iSUBC0a76#EF8:;k;#A#A7;8:9<;i?%27476#DIDC;i459<BCDIBC^`^`?@9<;iA767E]#DIBH?@DC9<EJBf?@05]#;#DCBI[Ud 476#8:9<? =@;#07a76#07^`BI;#076 479<BIDC6A76#EH?@a76#EJ6a7?@DI;#EFB«A7;78LBI9<BIa7B«O#B δφµ 076#DIDC607;#8:9<EF6=@;#0#O#BI^`BC;#05B CAPITOLO 1. 12.

(66) 8:A76#EFBIGR6#079<?@DIBT8:9<?@07O#?@EJOVS<ïõ β ~ïõJ[UdTö?cEJ;#9<?@^jBI;#076 δφµ O#BIA76#07O76VO#?@DIDCIBI079<6#078:BC9<î O#6#DIDCI?@07=@;#EJ?@]#]#BI;6#g2747BC05O#BCgDI?-O#6#9<6#EFGBI07?@^_BC;#076.8:A76#EFBIGR6#079<?@DC6.O#B δφµ bU;#EF07BI8:=@6 4707?cGRBI8:47EJ?cO#BIEF6#9<9M?cO#67BGR;#GR6#079<BTO7Bb<;7EF^`?cO#BT?@05=@;#EF?@]7]#BC;7de\67O#BC?@GR;#gT?LO76#8:8:;#gTBID A7EF;#=@67O#BCGR6#079<;>A767EO#6#9<67EJGHBI07?@EJ6 δφµ d °6#EBIDh05;#8:9<EF;k8:BI8:9<67GR?@gfDI?O#6#058:BI9<î8:47A76#EJb<BC=@BQ?@DI6i9<;#9<?@DC6iO#BH6#076#EJ]#BC?.DCBQª#6#EJ?8:B ;#9<9<BC67076þBC079<67]#EF?@07O#;þDI4707]#; àDC?®8:;#GRGR?®O#67DV=@;#079<EFBIª#479<;þ6#DI?@8:9MBI=@;+SU8:67=@;#07O#; 9<6#EFGRBI076O#6#DIDI?>SÊ´_Zd Y[U[\6VO#B27476#DIDI;GH?@]7076#9<BI=@;SUO?@9<;O#?@DIDI?>SÊ´`\d [U[Ug6V8:;#GRGH?@07O7;BID =@;#079<EFBIª#479<;>8:47A767EFb<BI=@BC?@DI6ÛO#?@9<;>O#?@DQDC?hSÊ´`dIêï#[ å. =. ∞ 0. 1 2. ä. 22. á φ á.â. 2. −. 1 µ 0 χÞ 2. (ã æ`ç è φ ) á.â 2. +. à ÞJß (φ Ý ). SÊ´`dIêô[. ö?h8:;#DI47^_BC;#076 φS½àÊ[Z=@6#EJ=@?@9<?Û h27456#DCDI?f=@N76>GBC07BIGBC^_^`?ÛBIDPb<4707^`BC;#07?@DI6Md*?@DP=@?@DC=@;#DI; O#6#DIDC6>a7?@EÀBC?@^_BI;#07BIgu;#9<9<6#05BI?@GR;>DCI6#2747?@^_BI;#076>O#BX4@DI6#EJ;#¬Kü?@]#EF?@05]#6>076#DKa7;#DC47GH6 ï. 22. í 2 φ íî 2. ð 1 µ0 χ 2. −. ì. 2. éSêZë 2φ. =0. SÊ´`dIê Y[. =@;#03DC?h=@;#05O#BI^`BI;#076>?@DK=@;5079<;#EF0#;38L45DCDI?f8L45A76#EFb<BI=@BC6cà±óVï −. ÷. õ φ 22 õ`ö. ô. ó. SÊ´`dIêW[. ∂ òó = ∂φ ñ. =0. 74 6#8:9<?=@;707O#BC^_BI;#076?@D=L;#079<;#EF07;ò678LA7EFBIGH6DIC6#2547BIDIBCª7EFBI;#g8:47DIDI?y8L45A76#EFb<BI=@BC6Üà>óñïg 9<EF?cBIDTGR;#GR6#079<;O#BTb<;7EF^`?c6#DI?@8L9MBI=@;VO#;7a7479<;V?@DIDC6²BC059<6#EJ?@^`BC;#05B=@;#0²DC6GR;#DI6#=L;#DI6VO#67D a7;#DI47GH6SU9<6#EFGRBI076y?²8jBI07BI8:9<EJ?BI0SÊ´`dIêW[[s6y27476#DIDI;yO#B?@07=@;#EJ?@]#]#BI;#g 6#8:6#EF=@BI9M?@9<;yO7?@D 8:47ª#8:9<EF?@9<;cSU9<6#EJGRBI076c?hO76#8:9<EJ?ÛO7BoSÊ´_dCêW#[[Udoü?c¤ ¦U5TÞ7#à`à`Û§#u@á# L_à`hR7T I@jg =@N76>BC05O#BI=@?fDI?fDC4707]7N76#^`^j?h=@?@EJ?@9<9<6#EJBI8:9MBC=@?fO#6#DIDI?hO7BI8j9<;#EF8:BI;#076#gK hO#6#bMBI07BC9<? ú SÊ´`dIê | [ ùξ = û 1 µ χø ö?hSÊ´`dI.ê Y[ZO7BCa76#059<*? ÿ φ 1 SÊ´`dI.ê [ ξ − ü,ý þ 2φ = 0 22. 0. 2. 2. ÿ. 2. 2. K6²GR;#DI9<BCA7DIBI=@N7BC?LGR;²6#079<EJ?@GRª#BoBuGH67GHª7EJBA56#E§. . A7?@8:8:?@]#]#BIgu;#9<9<6#07BI?LGR;>DCQ672747?@^`BI;#076>6#2747BIa7?@DI6#079<6φ ξ 2. φ. 2. −

(67). 2. §#à6²BI079<6#]#EJBC?LGR;#goO#;#A7;²8L67GHA7DIBI=:B. φ =

(68) . SÊ´`dIê.[. K47b<b<BI=@BC67079<6#GR6#079<6+DC;7079<?L07;+O#?@DCDI?®8:47A76#EJb<BC=@BI6¢àió. #ï gyBIDyO7BIEF6#9<9<;7EF6+8jB?@DIDIBI076#? 8:;#07;#g 4707BIbU;7EFGR6#GR6#079<6DI4707]#;yBCD =@?@GRA7;#dZü6y=@;#07O7BC^`BI;#07B ?@DZ=@;#079<;#EJ07;A76#Ehà A76#EF=@B\/@g φ ó ïi6!§ φ"½§#àÜó!ïk6#gH2747BI07O#BIgf;79<9<6#07BI?@GR;k=L;#8j9<?L059M6ó!ïdH→ö?%∞ SÊ´_dCê.[ O#BCa56#079<*? dφ sin φ SÊ´`dI.ê ~[ =± dz. CAPITOLO 1. ξH. 13.

(69) #O ;#a76BIDRO#;#A7A7BI;8:6#]#07;iBC05O#BC=L?%DI?%A7;#8:8:BIª7BCDQBI9<îñO5BR4707?-EF;#9<?@^`BC;7076O#6#DRO#BIEJ6#9<9<;#EJ6 ;#EF?@EJBC?3;²?@059UBI;#EJ?@EFBI?u8L6 β ~ï#õFgoDC?3EJ;#9<?@^jBI;#076²;EF?@EJBC?3SU8:6#]707; − R0767DCDI?>SÊ´`dCê.~[U[Ug EF?@A7A#EJ6#8:6#079<?@9<?BC0 ³KBC]747EF? ´`dIWgk b<?@a7;#EJBC9<?6#0767EF]#6#9<BI=@?@GR6#079<67dk/Ä08:6#]#47BI9<; =@;#078:BCO76#EF6#EJ6#GR;l8j6#GRA7EF6k27476#8:9<?8:;#DI47^`BC;7076#dfüI6#2747?@^`BI;#076lSÊ´_dC.ê ~[VA74 /i678:8:67EF6 BC079<67]#EF?@9<?h8:6#A7?@EJ?@07O#;>DI63a5?@EFBI?@ª#BCDQBIgK6#O3BIDKEJBC8:47DI9M?@9<;3* tan. φ(z) 2. = tan. φs 2. exp −. z. ξH. SÊ´`dIôï[. δφ(°). O#;#a76 φµ .DII?@07]#;#DI;kBI08:47A76#EJb<BC=@BI6iBI0iA7EJ6#8:6#07^`?.O#6#DH=@?LGRA7;#gf8:;#DC45^jBI;#076O#6#DIDI? =@;#07O#BI^`BC;#076>?@DP=@;#079<;#EJ07;>SÊ´`dCêW[Ud ö?kDC4707]7N76#^`^j?kO#B3=@;#6#EJ6#07^`?lGR?@]#076#9<BQ=@?@g>O76#b<BI07BI9<?lO#?LDIDC?kSÊ´`dIê | [UgcN7?k470!EF47;#DI; b<;#07O#?@GR6#079<?@DI60767DCDQ?O#678:=@EJBC^_BI;#076O76#DZ=@;#GRA7;#EF9<?@GR6#079<;GH?@=@EJ;#8:=@;#A7BI=@;O767D«X«ü© 6-BC07O5BC=@?ÜDIC;#EJO#BI076O#B±]#EJ?@07O#6#^`^`?éO76#DCDI;8:A76#8:8:;#EJ6-O#6#DIDC;8:9<EF?@9<;-O7BI8:9<;#EF9<;-a5BC=@BI07; ?@DCDIIBI079<6#EJb<?@=@=@BC?Ld K6ìi c?@ª#ª#?@8:9M?@07^`?cBI079<6#078:;VBI0GR;#O#;=@N76 ξ 8LBI?cGR;#DI9<;VGRBC07;7EF6 O#6#DIDC;i8LA56#8:8:;#EF6!§O#6#Df=@?@GRA7BC;7076kO#BfXZü©gf]#BCîñ?A5;#=5N7BfGH45DC9<BIA7DCBfO#B ξ O#?@DIDC? 8:47A76#EFb<BI=@BI6O#B-8:6#A7?@EJ?@^_BC;#056#g-DCI;#EJBC6#079<?@^`BI;#076O#6#í D-O#BIEF6#9<9<;7EF6 ÚA7EF?@9<BI=@?@GR6#079<6 A7?@EF?@DIDC67DC?( ?@D²=@?@GRA7;#d°u;#076#07O#; b ó¡ô#Zd ~ ⋅ ´j*ï x ©sg χQ ó´_dC.ô Y}M´`jï x0¥6 ó | dI ô (}1´`ï ë y8 "UGRg!8:B(;#9<9<BI6#076 ê\d Y GHd(/Ä0³uBC]#47EJ? ´`d | EFBIA#;#EJ9<BC?@GR; DCI?@07O#?@G6#079<;#gO7?@9<;òO#?@DIDQ?SÊ´`dIôï[<ξg O#B δφ ≡ β −µ φ BC0b<4707^`BC;7076òO76#DEF?@A#A5;EF9<;éà " ξ 076#Bu=@?L8:BPO7Bu?@07=@;7EF?@]#]#BI;>b<;#EJ9<6>6>O#6#ª#;#DI6#d. µ:¶ · ¸¹<ºV»½¼ ¾.i#Ç7É ÎMÌ

(70) ÈUÇ7ÐIÅ²ÉÊÈ Ë ËÄÎÛÉ_È5ÖIÁ1ÎMÆ½Á1ÅÇ5ÈcÉÊÈ Ë

(71) ÉUÁ ÓFÈÊÐCÐCÅÓÈcÉ_Î1Ë Ë¬ ÎFÂJÂÀÈRÏ ÎFÍMÁ Ë1ÈRË1Ò<ÇÊØ#ÅRÁ Ë

(72) ÍFÎMÌ ÃÊÁ1ÅUÇ7È Ô @Ç7Ð ÓÎMÌao È ËÄÈÍFÒUÓLÖÈ