# Hermitian operator

1. Mar 14, 2012

### sm09

what is it?

2. Mar 14, 2012

### earlofwessex

an operator that is hermitian!

in a matrix representation, it means that the diagonal Mii is real, and any Mij is the complex conjugate of Mji. this gives the hermitian conjugate of M (transpose and conjugate) is itself.

it represents a measurable quantity in QM.

ps.
am i right?

Last edited: Mar 14, 2012
3. Mar 14, 2012

### sergiokapone

This question is well enough described in a any QM textbook. You do not make much effort to look there. In simple, Hermitian operator is the observable represetation, or if not rigorously speaking, it reflects the measurement procedure in a some quantum state. For example, let we have an spin-up directed electron state $\left | + \right>$. Measurement of the z-directed spin by $\hat S_z$ in this state is reflected in the equality $\hat S_z \left | + \right> = +\hbar/2 \left | + \right>$. This mean the result you will get is $+\hbar/2$. A key feature of a Hermitian operator is real numbers of their eigenvalues.

Last edited: Mar 14, 2012