Physics 212 Problem Set One
1. Perturbed Square Well
Consider a onedimensional system consisting of a particle of mass m and charge e in the potential well V (x)
shown (see gure).
6
6
V (x)
6
a
2
a
4
a
4
0
b=
?

a
2
2 h2
8ma2
x
The potential energy f
Physics 212: Problem Set 12
1. Show that the swave phase shift for scattering o a potential of the form
V (r) =
C
(r r0 ) 2 ,
h
2
where C is a constant and (r r0 ) is a Dirac delta function, gives the phase shift relationship
tan(kr0 + 0 ) =
tan(kr0 )
.
Physics 212 Problem Set 11 Spring 2010
1. Scattering in 1D.
(a) Consider a single potential step. The potential is zero from x < 0 and a constant V0 for x > 0. A particle
of mass m is incoming from x < 0 with energy E = h .
i. Write the Schrodinger equat
Physics 212 Problem Set 10 Spring 2010
1. Find all of the allowed spectral terms for the 1s2 2s2 2p3 conguration by proceedings as follows:
(a) Why are the spectral terms dictated by only the 2p3 part of this conguration?
(b) Form the analog of our naive
Physics 212 Problem Set 9 Spring 2010
1. Permutation operator
(a) Show that if
O = Pjk OPjk 
,
(1)
then
O = Pjk OPjk 
,
(2)
where  and  are each identical particle wavefunctions, Pjk is an interchange operator, and O is an
observable for an
Physics 212 Problem Set 8 Spring 2010
1. Show that the relationship we obtained from imposing the condition that our atoms are in a steady state
of thermal equilibrium at temperature T and the applied radiation eld is also in thermal equilibrium at
temper
Physics 212 Problem Set 7 Spring 2010
1. The Zeeman Eect with Nuclear Spin
An external magnetic eld is applied to a system with nuclear spin I and electron total spin J . The zeroth
order Hamiltonian then gains the term
H(1) = AI J J B I B.
Applying the m
Physics 212 Problem Set 6 Spring 2010
1. More Fine Structure for the Hydrogen Atom.
(a) For levels n = 1, 2, and 3, evaluate the eect of the spin orbit coupling. Sketch the corrected levels.
(b) Combine the three ne structure corrections and show that for
Physics 212 Problem Set 5 Spring 2010
1. CTDL Chapter 10 problem 2.
2. Numerical Eect of the Lowest Order Relativistic Correction on Hydrogen Energy Levels.
Evaluate the unperturbed energy levels n = 1, 2, and 3 for the hydrogen atom. Sketch and label th
Physics 212 Spring 2010 Problem Set 4
1. CTDL Ch. X problem 1
2. CTDL Ch. X problem 3
3. Show, using a plane wave as your original eigenstate, that the momentum operator generates a translation in
space. Prove that a unitary operator U may be written in
Duke University
Physics Department
Physics 305
January 14, 2010
Assignment No. 1 (60 pts)
(due in class Jan262010)
Problems:
1. [20 pts] The Lagrangian density for a vector eld with mass M is written as:
1
1
L = ( A A )( A A ) + M 2 A A
4
2
(1)
Use the