Chem 532: Problem Set #4
Due in class: Friday, Oct. 11th
(1) Show that y , z = i x and 2 , x = 0 .
(2) Given that j+ = jx + ij y and j = jx ij y , show that
(a) j 2 , j = 0
(b) jz , j = j
(c) j+ , j = 2jz
(3) Using the real-valued spherical harmonics defi
Chem 532: Problem Set #1
Due in class: Wednesday, Aug. 28th
(1) The energy density per unit volume (between and +d) of a perfect blackbody
can be written in terms of the Planck distribution function as
hc
8 hc e kT
dE = 5
d
1 e hc kT
(a) Show that the e
KEY
Chem '532: Second Exam ' Friday, November 15, 2013 (80 pts. possible)
Please budget your time carefully and show all work for partial credit (see last page for data & eqns.).
(1) (20 pts) Consider a paramagnetic atom with nuclear spin angular moment
Chem 532: Problem Set #2
Due in class: Friday, Sept. 13th
(1) For an operator that does not explicitly depend on time, the time dependence of its
expectation value is given by the Ehrenfest Theorem:
dA
d
i
A = H , A
dt
dt
Show that the rate of change of
Chem 532: Problem Set #3
Due in class: Friday, Sept. 27th
(1) Consider a 1-dimensional-box potential such that the bottom of the box has a step at
the midpoint, where the step height is Vs and the two sides have infinite potential. Use
solutions of the tr
Chem 532: Problem Set #4
Due in class: Wednesday, Oct. 23rd
(1) Determine all 9 coupled states (and their expansion in terms of uncoupled states) for
the case of two p electrons. (Hint: follow the procedure used in class for the case of
two d electrons, y