Problems U Can Do!
Mark Strother
May 6, 2013
Standard disclaimer: This is not an attempt to simulate the conditions of the nal. In
particular, the length, diculty, subject matter, and appearance of the problems are not in any
way intended to recreate the
HW #5 Solutions
Mark Strother
February 21, 2013
Disclaimer: The notation for angular momentum addition is notoriously tricky. Too much labeling
will obfuscate the physics; too little labeling leaves ambiguity. Since I cant help feeling responsible for
you
HW #7 Solutions
Mark Strother
March 8, 2013
Were doing perturbation theory now. Youre going to see the symbols and all over these solutions,
which mean much greater than and much less than respectively. They are standard when discussing
quantities that fo
HW #4 Solutions
February 15, 2013
Chapter 10
7. Spin ipping at resonance
2
(a) To get c (t), simply use = ( 0 )2 + 1 . We know that c (t) = a (t)ei0 t/2 ; from
the requirement that |c+ (t)|2 + |c (t)|2 = 1, we nd that |a+ (t)|2 = cos2 1 t/2. Therefore,
we
HW #3 Solutions
February 5, 2013
1. Eigenvalues and Eigenvectors
(a) Denote this matrix M = aI + b . We need to solve the characteristic equation
I) = 0:
det(M
a + bz bx iby
bx + iby a bz
=0
This yields
(a )2 b2 ) (b2 + b2 ) = 0
z
x
y
Solving for , we h
HW #6 Solutions
Mark Strother
March 3, 2013
1. Quantum Correlations
(a) If we imagine the opening angle is approaching zero, then Alice and Bob are actually measuring
along the same axis, regardless of whether a measurement is performed along the 1-,2- or
HW #9 Solutions
Mark Strother
April 1, 2013
Chapter 3
3. Energy levels of anharmonic oscillator with WKB
The expression for the number of wavelengths between the classical turning points cfw_x , x+ is
2m x+
dx E bx4 .
N=
2
x
Making the change of integrati
HW #10 Solutions
Mark Strother
April 4, 2013
Chapter 14
3. Densities of states of the degenerate electron gas in two and three dimensions
The energy eigenvalues of the degenerate electron gas are given by
(2D)
Enx ny = (n2 + n2 )
x
y
22
(3D)
Enx ny nz = (
HW #12 Solutions
Mark Strother
April 30, 2013
Chapter 15
5. Lifetime of 300
(a) The only states allowed by selection rules are 21m (m = 0, 1).
(b) The bulk of this calculation is determining the value of the matrix element 300| z |210 . The x
and y integr
HW #11 Solutions
Mark Strother
April 19, 2013
1. Weak decay of 3 H 3 He, CORRECTED
This is a sudden change perturbation; the transition amplitude is simply given by the overlap of the
initial state with the nal state. We are asking what the probability of