Conserved quantity in quantum mechanics ↩

Metadata

shorthands: {}
aliases: [Constant of motion in quantum mechanics]
created: 2021-12-11 15:58:06
modified: 2022-01-10 04:13:03

We have seen that if we want to find the time derivative of an observable, an operator

acting on the appropriate Hilbert space

, we can get it by looking at its commutator with the Hamiltonian operator.

Based on this, if they commute, then the time derivative is also zero. This means that the expectation value of does not change throughout the time-evolution of the system according to the Schrödinger equation. In this case, we call a conserved quantity or constant of motion.