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Meccanica Quantistica 22 Giugno 2017

PROBLEM A

Let us consider a particle with spin 1/2. We measure the observable S

x

+ S

z

. 1) Calculate the possible measured values.

After then we measure the observable S

y

.

2) Calculate the possible measured values, the probability to get them and the final states in which the system can be found.

PROBLEM B

Consider a particle with mass m in a two dimensional infinite potential well with size [0, a) × [0, a). At the time t = 0 the particle is described by the state,

ψ(x, y) = N sin

 πx a



sin

 πy a

 

1 + 2 cos

 πx a



Calculate, at the time t,

1. The average value hEi

t

and the dispersion ∆E

t2

of the energy.

2. Calculate the corrections to the first order in ε for the ground state and the first excited state under the perturbation V = εy.

1

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