Hausdorff expansion ↩

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created: 2021-12-12 22:14:36
modified: 2022-01-10 04:13:03

Given two operators acting on the Hilbert space

and

, the following identity is always true:

Where the brackets mean commutators.

If and commute, then the result is just simply .

Derivation

We can get the identity by expanding the exponential functions and calculate term by term: