Quantum mechanical time derivative ↩

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created: 2021-12-11 15:19:45
modified: 2022-01-10 04:13:04

From the time derivative of expectation value in quantum mechanics, we can define a time derivative on operators this way:

Where is an (optionally time dependent) observable acting on the appropriate Hilbert space and is the Hamiltonian operator.

This formula is easy to derive using the Heisenberg picture of time evolution.