The sum in problem 6.4a
The sum we need to complete is,
S=
n
mn
2
1
.
m2
This can be simplified using partial fractions,
1
1
1
1
1
1
S=
n m + n + m = 2n n m + n + m .
mn
2n m n
mn
The sums can each be broken into th
This problem is based on the paper Average value of position for the anharmonic
oscillator: Classical versus quantum results by R. W. Robinett in the American Journal
of Physics (vol. 65 (3) March 1997 pp.190-194). You may want to get a copy of this
paper
Problem 7.14 Comments
1. Use the ground state hydrogen wave function as the trial function but replace the
Bohr radius a with a variational parameter, b,
1 r
= ( b 3 ) 2 e b .
2
a2
b
a
2. You should find H = E
Dipole Matrix Elements
We really need to get good at the so called dipole matrix elements. In a few weeks
well learn how to do these in general. For now well settle for understanding some
of their symmetries.
Problem 18 Clarification
Here is my best effort to clear up the question.
1. Draw an energy level diagram showing the Bohr energies for the n = 3 and n =2
states. Save room to draw the fine structure l
Problem 621 Clarification
Lets agree to solve this problem be as described here.
1. Build a table like the one below.
State
HB (E2)
Hfs (2E2)
gJ
1
4
33
2,1, 1 , 2 , 2
16
1
2
3
The EPR Experiment
The article "Is The Moon There When Nobody Looks ? Reality and Quantum Theory" by N. David
Mermin (Physics Today, v38, pp 38-47, 1985) contains the cleanest description of an experiment that exhibits
different predictions for a "complet
Feynmans Proof of Maxwells Equations
Get a copy of the paper Feynmans Proof of Maxwells Equations by Freeman Dyson
published in AJP 58 (3) March 1990. This proof has many interesting points, not the least of which is
that Maxwells Equations appear to be d
Problem 6.6*
Given that a 2x2 portion of the unperturbed Hamiltonian matrix is degenerate, it might
look like,
E 0 0
0
.
H =
0
0 E
(a)Write the eigenvectors and their corresponding eigenvalues for H0.
The perturba
The Zeeman Effect - Calculating Splittings and Relative Intensities
In Phys 227 you might conduct an experiment to examine the splitting of the "mercury green line" in
the presence of a magnetic field. The green line has a wavelength of 546.1nm and is kno
Physics 435B - Partial Wave Analysis
The quantum scattering problem must have solutions of the form given in eq. 11.12,
e ikr
( r, ) Ae ikz + f ( ) .
r
It is our job to write this as a linear combination of the eigenfunctions of Schrodinger's
Equatio
Gauge Invariance Issues and the Aharanov-Bohm Effect
Replacing p p + qA in Schrodingers Equation has some interesting consequences due to
the vector potential for a given magnetic field is not being unique. Changing from one vector
potential to another is