Classical Physics versus Quantum Mechanics
Classical physics:

Observables are numbers.

All observables are independent.
Quantum mechanics:

Observables are operators that act on the wave
function psi to generate a number.

Most observables are independent.
is
called the commutator

Conjugate observables are not independent.
Conjugate observables (potential/momentum) must have a nonzero commutator to quantize a field.
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