Eigenvalues of Hermitian operators are real ↩

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created: 2022-01-05 15:22:07
modified: 2022-01-10 04:13:04

Statement: The eigenvalues of a Hermitian operator are real ().

Proof

Let be an eigenvector of . Then

And the complex conjugate:

Since is Hermitian, , so:

Which can only be true if is real.