Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Equal to its own transpose conjugate.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

The observable is conserved if and only if the equations of motion are invariant under the transformations generated by the corresponding [Hermitian] operator
Special Post: Noether’s First Theorem – Emmy Noether for Ada Lovelace Day

Hermitian operators in the Hilbert space associated with a system represent physical quantities, and their eigenvalues represent the possible results of measurements of those quantities.

There are many cases in quantum mechanics where the Hamiltonian functions that represent the total energy of mechanical systems imitate those of classical mechanics, but with variables like those that stand for position and momentum replaced by Hermitian operators.

The only thing which is real are the eigenvalues of Hermitian operators.

I tend to think of the expectation of a Hermitian operator as observable.

Strictly speaking an observable in QM is determined by a Hermitian operator.

So is Hermitian and has units of frequency, so it must be some kind of frequency observable.

That makes the operator on the right side Hermitian.

Things which are directly observable might simply only be those things which are associated with Hermitian operators in quantum mechanics.

The question might be asked whether the electric or magnetic field in quantum mechanics are Hermitian operators.
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