Bilkent University
   
Department of Physics
PHYS 326 Quantum Mechanics II
Spring 2007 Homework Assignments
Homework Policy
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Homework 1: (due Feb. 6, 2007)
Find the angular momentum related matrices Sx,
Sy, Sz, S+, and
S- for a spin-5/2 particle. Show that the spin matrices
obey the commutation relations.
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Homework 2: (due Feb. 20, 2007) Problems 4.34, 4.36, and 4.59 in the textbook.
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Homework 3: (due March 13, 2007)
Consider an electron in a one-dimensional harmonic oscillator potential.
An electric field E is applied to the particle.
The potential energy of the system now has an additional term of the form
H1=eEx.
- Find the first order change in the energy of the ground state.
- Find the first order change in the wavefunction of the ground state.
- Using the ground state wavefunction corrected to first order, find the
expectation value of x.
- Write the energy of the system as
H=k(x-x0)2/2+E0 where
x0 and E0 are constants related
to the perturbing field E.
What do they physically correspond to?
How are they related to the results you found in the previous part?
The following problems are assigned to those students who did not attend
class on Thursday, March 8th.
Other students may turn them in for extra credit:
Problems 6.1 and 6.2 in the textbook.
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Homework 4 (due March 20, 2007)
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Homework 5 (due March 27, 2007) Calculate the first order shift in
the ground state and the first excited state energy levels of a charged particle
in a cubic box of size a due to the Stark effect. Take the external
electric field in the z direction, parallel to one of the edges of
the cube. Repeat with a perturbation of the form cxy where c
is a constant.
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Homework 6 (due May 8, 2007) Calculate the lifetimes of the first,
second, and third excited states of an electron a one-dimensional box of
size a. Note that for the second and third excited states, you will
have to find the transition rates to more than one lower energy state. For
the third excited state, what is the relative probability that the electron
will go directly to the ground state?
Check the Student BAIS
system for your homework grade. In some cases, you may be able to
re-submit your homework to the assistant with corrections and
improve your grade.