Introductory statistical mechanics for a microcanonical ensemble (a.k.a. constant energy, no exchange of heat or work with environment) claims that all microstates in the momentum–location phase space are equally probable to occur.
But for a harmonic oscillator, the particle is more likely to be found at points of lower momentum, because the particle spends more time in those locations.
Here is an excerpt from Chapter 5 of Greiner’s Thermodynamics and Statistical Mechanics showing the example of the microstates in phase space of a 1D harmonic oscillator:
It seems like common sense that those microstates have a differing probability of occurrence than each other, because the probability of finding the particle at the various locations is not equal.
Here is an excerpt from Chapter 2 of Griffith’s Introduction to Quantum Mechanics showing this distribution:
What am I misunderstanding here?