I am currently studying the Heisenberg Uncertainty Principle, and - while I have understood the general idea - I am struggling with the role of momentum within the principle.
I know momentum as mass times velocity, or - for photons - energy over velocity. I have always related to momentum as an indirect indicator of energy, as both mass and velocity are related to energy (although that interpretation might be wrong, because I was never forced to analyse it until stumbling upon the Heisenberg Uncertainty Principle, and rather simply used it as a comfortable tool to perform certain Classical computations).
Intuitively, though, it feels more logical to use velocity within the context of the Heisenberg Uncertainty Principle. I know intuition is a very bad methodology with Quantum Physics, and often one simply has to accept the way nature works. Nonetheless, I would like to know if there is any logical explanation that could make the role of momentum here a bit easier to understand. What is it an indicator of? Does it indicate energy levels? Or does momentum here stand for something else?