Hermitian operators represent physical variables in quantum mechanics. Physical variables must have real expectation values, which implies that the operators representing them are equal to their own Hermitian conjugate. Operators with this property are called Hermitian operators. The document goes on to define Hermitian operators and prove that their eigenvalues are real and their eigenfunctions are orthonormal.

4. Hermitian Operators
A physical variable must have real
expectation values (and eigenvalues).
This implies that the operators representing
physical variables have some special
properties.
By computing the complex conjugate of the
expectation value of a physical variable, we
can easily show that physical operators
are their own Hermitian conjugate.

6. Operators that are their own
Hermitian Conjugate are
called Hermitian
Operators.

7. Hermitian
Operators

13. Properties of Hermitian Operators
Definitions

14. Proof that eigenvalues are

16. Proof that eigenfunctions are orthonormal

18. Thank
You