HW 11.1. In the first Born approximation, calculate the differential cross section
d!
for
d"
the Gaussian potential
2 2
V ( r ) = V0 e !r /a .
Give your answer in terms of the momentum transfer q and the various constants.
HW 11.2. (a) Again in the first
HW 12.1. A small perturbation ! x 4 is added to the Hamiltonian for the harmonic
oscillator. (This represents the anharmonic effects in a real system.)
(a) Calculate the first-order correction to the energy eigenvalues, ! En .
Give your answer in terms of
Physics 606, Quantum Mechanics, Exam 2
Please show all your work.
(You are graded on your work, with partial credit where it is deserved.)
All problems are, of course, nonrelativistic.
Vectors here are marked with arrows.
!2
L etc. here are operators in t
Physics 606, Quantum Mechanics, Exam 1
NAME_
Please show all your work.
(You are graded on your work, with partial credit where it is deserved.)
All problems are, of course, nonrelativistic.
Vectors and matrices are in boldface.
!
p
According to a future
1. (15) A particle is in an eigenstate of the angular momentum operator Zz:
Zzlm)= mhlm) .
Calculate the expectation values of 2x and Zy , (m|ix|m) and
[Hint One method involves using the commutation relations for the angular momentum operators]
A A A A
Physics 606, Quantum Mechanics, Final Exam
Please show all your work on the separate sheets provided (and be sure to include your name).
You are graded on your work on those pages, with partial credit where it is deserved.
All problems are, of course, non
Physics 606, Quantum Mechanics, Exam 1
NAME_
Please show all your work.
(You are graded on your work, with partial credit where it is deserved.)
All problems are, of course, nonrelativistic.
1. The operator a of the harmonic oscillator is defined by
m!
i
Physics 606, Quantum Mechanics, Final Exam
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1. Atomic transitions due to time-dependent electric field.
Consider a hydrogen atom which is in its ground state for t < 0 . For t > 0 it is subjected to a spatially
uniform electric field
E 0 e!t /"
which
Physics 606, Quantum Mechanics, Exam 2
NAME_
Please show all your work.
(You are graded on your work, with partial credit where it is deserved.)
All problems are, of course, nonrelativistic.
_
1. In this problem, start with the following two equations for
Physics 606, Quantum Mechanics, Exam 2
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1. Fun with hydrogen
For an electron in the hydrogen atom, the normalized ground state is 100 , with wavefunction
2 "r /a0 1
! 100 = 3/2 e
a0
4#
which satisfies the time-independent Schrdinger equation
e2
. (1)
Physics 606, Quantum Mechanics, Exam 1
NAME_
Please show all your work.
(You are graded on your work, with partial credit where it is deserved.)
All problems are, of course, nonrelativistic.
_
1. In one dimension, a free particle with mass m is perturbed
Physics 606, Quantum Mechanics, Final Exam
NAME_
Please show all your work.
(You are graded on your work, with partial credit where it is deserved.)
All problems are, of course, nonrelativistic.
_
1. Consider a particle in one dimension with position oper