Short lecture Hermitian operators in quantum mechanics.
Measured values of physical properties in quantum mechanics must correspond to eigenvalues of their quantum operators. Physical properties have real number values, thus the eigenvalues of these operators must always be real. Hermitian operators are guaranteed to produce real eigenvalues, as defined here for eigenfunctions and general functions. Every operator in quantum mechanics is required to be a Hermitian operator.
Notes Slide: http://i.imgur.com/AJ7KXOG.png
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