Hermitian operators in quantum mechanics constitute the mathematical formalism wherein physical observables correspond to self-adjoint linear operators defined on a complex Hilbert space. This principle ensures that eigenvalues representing measurable quantities are strictly real and guarantees unitary time evolution through the preservation of the inner product structure. The domain is specifically theoretical physics within the framework of non-relativistic quantum mechanics, establishing the foundational link between abstract operator algebra and experimental phenomenology.
Explains Hermitian operators, why their eigenvalues are real, and their role representing observables in quantum mechanics.