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In Quantum Mechanics, why is it that a self-adjoint operator is linked to an observable? What makes it measureable? And why isn't a non-Hermitian operator linked to an observable?

Also, what type of observables are we talking about here? Particles?

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up vote 2 down vote accepted

The is a theorem that says Hermitian operator are associated to real eigenvalues.

Since eigenvalues correspond with our measure values and they are real, this means that it makes sense to have hermitian operators as observables.

Also, what type of observables are we talking about here? Particles?

Observables are magnitudes we can measure: position, momentum, angular momentum, charge, etc.

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