The canonical commutation relation between the position operator and momentum operator is one of the defining equations of quantum mechanics. It's what leads to the Heisenberg uncertainty principle, that even if you know the quantum state (or wavefunction) of a particle, you can't precisely determine its position and momentum at the same time.

In this video, I'll show how the CCR follows by defining the momentum as the generator of spatial translation symmetry. Along the way, we'll take a crash course in the fundamentals of quantum mechanics.

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