What is an example of a quantum mechanics practice problem?

measuring a subatomic particle's true direction and speed.

Since the actual probes use the same kind of particles to measure, it's actually like trying to measure a baseball ball's position and speed by throwing another ball at it; the ball that gets hit by the "measuring" ball will change its trajectory and speed when it hits it the first time. This means that if we measure a particle, we can only determine its immediate position; we can no longer determine what the particle's natural course would have been. As a result, a second measurement will retrieve information that has already been altered by the first measurement.

This is similar to requesting an example of a practice problem in classical mechanics: there are a ton of examples available because the subject covers a wide range of topics.

Exactly what level of QM you are looking for will determine how easy or difficult it is to provide a good example of a practice problem; it could be as simple as normalizing a basic quantum state vector, or it could be more involved and involve time-dependent systems with time evolution, harmonic perturbation, etc.

This problem is taken from Ira N. Levine's book Physical Chemistry, 6th edition, page 613, Example 17.4. The book is available for purchase here.

Issue:

c. Locate hatBhatA-hatAhatB.

Please feel free to leave a comment if you would like me to write the solution.

An example of a quantum mechanics practice problem could be calculating the probability of finding a particle in a particular state given its wave function, or solving for the energy eigenvalues and eigenfunctions of a quantum system, such as a particle in a one-dimensional box.