Wissink
Fall 2013
P454 Quantum Mechanics II
Problem Set # 2
SOLUTIONS
1. De Generalization of De Generacy
In class, we argued that the rst-order corrections to the energies of d degenerate states
are given by the eigenvalues of the matrix Hij , and the ei
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 9
SOLUTIONS
1. This Time For Sure!
So, here is last weeks leftover. Please do Problem 11.5 on page 407 one of the classic
problems in phase shift analysis, with lots of nice insights along the way.
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 1
SOLUTIONS
1. Making Waves, Down on the
In class, we considered a 1-D innite square well, extending over the range 0 < x < a, but
with half of the well at a potential energy of V0 . To rst order,
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 3
SOLUTIONS
1. Fine By Me
The nal expression we obtained for the ne structure of the hydrogen atom had two
contributions, that just happened to be of the same size: a relativistic correction, and t
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 4
SOLUTIONS
1. SHO Me the Functional!
Consider the 1-D SHO, described by the familiar Hamiltonian:
H=
1
h
2 d2
+ m 2 x2
2
2m dx
2
We know that the true wave function for the ground state is a Gaus
Wissink
Fall 2013
P454 Quantum Mechanics II
Problem Set # 8
SOLUTIONS
1. Expanding, Well, . . . Suddenly!
Continuing our theme from the previous homework set . . . Consider once again an innite
square well, with one wall xed at x = 0. At t = 0 the second
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 7
SOLUTIONS
1. Spiraling Downward
In lecture, weve discussed two mechanisms for inducing downward transitions in atoms:
spontaneous vs. stimulated emission. For a system at some nite temperature T
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 6
SOLUTIONS
1. Im SHO Excited!
Consider a 1-D SHO, with the usual Hamiltonian
1
h
2 d2
+ x2
H=
2
2m dx
2
The system is prepared initially (at t ) in its ground state. The oscillator is then
subjec
Wissink
P454 Quantum Mechanics II
Fall 2013
Problem Set # 5
SOLUTIONS
1. Livin on the Ledge
Consider an innite square well potential in which half of the potential is higher than the
other half; more precisely, suppose
V0
for 0 < x < a/2
V (x) =
0
for a/2