# Hermitian Operator Proof - Question

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## Main Question or Discussion Point

Hi,

Why to do this proof is needed to compute the complex conjugate of the expectation value of a physical variable? Why can't we just start with $< H\psi \mid \psi >$ ?

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PeroK
Homework Helper
Gold Member
Hi,

Why to do this proof is needed to compute the complex conjugate of the expectation value of a physical variable? Why can't we just start with $< H\psi \mid \psi >$ ?
If that's a proof of anything, it escapes me.

Normally, one proves that the eigenvalues of a Hermitian operator are real and then attention is restricted to Hermitian operators for observables; even though there may be non-Hermitian operators with real eigenvalues.

Jd_duarte and dextercioby
Hi,

Why to do this proof is needed to compute the complex conjugate of the expectation value of a physical variable? Why can't we just start with $< H\psi \mid \psi >$ ?