Sources for hard Introductory Quantum Mechanics problems [closed]

Question

I have an upcoming undergraduate introductory QM exam. The teacher is known to hold grudge against classes of students he doesn't like, so in an act of spite he gives them the hardest problems he can find. This exam is in two weeks, and we pissed him off good :) .

I want to get ready and I ran out of problems, so I ask you to give me the hardest problems you know (and solutions if you can).

The problems should be solved analytically and the topics are the basic introductory QM topics: potential well, harmonic oscillator, hydrogen atom, scattering off constant and delta potentials, linear algebra + Dirac notation, angular momentum, etc...

So if you know of tough problems from unknown or foreign books, previous exams, previous homework or even self written problems, I would welcome them all. Solutions would also be very helpful. We could also discuss the problems and their solutions, can be fun.

Answer 1

The canonical resource for this is

• Flügge, S., 2012. Practical quantum mechanics. Springer Science & Business Media.

The original is in 2 volumes, possibly now combined into 1. If you can work through those, you can do everything. This is the backbone for preparing PhD exams in many North American programs.

Another source is

• Ter Haar, D. ed., 2014. Problems in quantum mechanics. Courier Corporation.

which is slightly easier.

For a serious undergraduate exam there is also

• Capri, Anton, Z., 2002. Problems and Solutions in Nonrelativistic Quantum Mechanics (p. 492). World Scientific

or

• Lim, Y.K., 1998. Problems and solutions on quantum mechanics (Vol. 6). World Scientific.

Lim is a compendium or PhD qualifying exams from major US universities. There are other texts like

• Constantinescu, F. and Magyari, E., 2013. Problems in quantum mechanics. Elsevier.

but this is nowhere as expansive as Flugge or Capri.