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.