Time dependence of expectation value in quantum mechanics ↩

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aliases: [Time derivative of expectation value in quantum mechanics]
created: 2021-12-11 14:55:48
modified: 2022-01-10 04:13:04

Let's consider a quantum observable represented by the operator

acting on the appropriate Hilbert space

and let

be a solution to the Schrödinger equation.

The time derivative of the expectation value will then be:

If we also take account of the optional explicit time dependence of the operator:

This shows that the Hamiltonian operator generates the time evolution of the system.

See also