Graduate Quantum Mechanics I
PHY505
Homework 1 Due: Friday, 3/16/2016, to TA
1. (a)
Problem 2, p. 109, Chapter 2, Gottfried & Yan.
(b)
Show that U 1 f (A)U = f (U 1 AU ). Therefore, if U is unitary, the unitary
transform of the function of an operator A i

Graduate Quantum Mechanics I
PHY505
Homework 4 Due: Friday, 4/15/2016, to TA
1. Problem 18, p. 239, Chapter 4, Gottfried & Yan. Assume the radii of the inner
and outer cylinders are a and b, respectively. Also assume the two ends of the
cylinder are at z

Graduate Quantum Mechanics I
PHY505
Homework 7 Due: Wednesday, 6/1/2016, to TA
1. Estimate the ground state energy of a helium atom by the variational principle.
Use the hydrogen like wave functions as the trial functions and confirm the results
given in

Graduate Quantum Mechanics I
PHY505
Homework 5 Due: Monday, 5/9/2016, to TA
1. (a.) Let R1 and R2 be two infinitesimal rotations parametrized with 1 and
2 , and K a three-vector. If K is the change induced in K by R =
R21 R11 R2 R1 , show that to leading

Graduate Quantum Mechanics I
PHY505
Homework 6 Due: Monday, 5/23/2016, to TA
Reading of the following weeks: Degenerate state perturbation theory (section
3.7(b), Time dependent perturbation theory (section 3.7(c) and (d), Variational
principle (section

Graduate Quantum Mechanics I
PHY505
Homework 2 Due: Monday, 3/28/2016, to TA
Each problem is worth 15 points in this assignement.
1. In lectures we have developed a method to compute the propagator < x00 t | x0 0 >
for a free particle. Apply the method t