I know that with an(adsbygoogle = window.adsbygoogle || []).push({}); operator the expectation value can be found by calculating the (relative) probabilities of each eigenvalue: square modulus of the projection of the state-vector along the corresponding eigenvector.Hermitian

The normalization of these values give the absolute probabilities.

Alternatively it's possible to calculate directly the expectation value by the compact formula <A>=<psi|A|psi>.

I got stumbled considering what adjustment to take in case of an operator that is.not Hermitian

In this case the eigenbasis is not orthonormal. But I feel that there should be some way to calculate the expectation value of the operator nonetheless.

Am I wrong? Or there's no meaningful way to define it in the non hermitian case?

If the procedure is more or less the same with some adaptation to make then:

Which projection to take? the components in the eigenbasis or the orthogonal projections of psi along the eigenvectors?

Is there an analog of the formula <A>=<psi|A|psi> that is correct in the non.orthonormal basis?

Any help appreciated

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help with expected value of non-hermitian operators

**Physics Forums | Science Articles, Homework Help, Discussion**