Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 11, Problem 11.36P

(a)

To determine

The classical position of the oscillator, assuming it started from rest at the origin (xc(0)=x˙c(0)=0).

(b)

To determine

Show that the solution to the time-dependent Schrodinger equation for this oscillator can be written as Ψ(x,t)=ψn(xxc)exp(i[(n+12)ωt+mx˙c(xxc2)+mω220tf(t')xc(t')dt]).

(c)

To determine

Show that the eigenfunctions and eigenvalues of H(t) are ψn(x,t)=ψn(xf) and En(t)=(n+12)ω12mω2f2.

(d)

To determine

Show that in the adiabatic approximation the classical position reduces to xc(t)f(t).

(e)

To determine

Show that Ψ(x,t)ψn(x,t)eiθn(t)eiγn(t) and check whether the dynamic phase has the correct form. And determine the geometric phase.

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