How can you prove that ladder operators are hermitian operators?

The hamiltonian operator is the observable corresponding to the total energy of the system. As with all observables it is given by a hermitian or self adjoint operator. This is true whether the...

A Hermitian operator is any linear operator for which the following equality property holds: integral from minus infinity to infinity of (f(x)* A^g(x))dx=integral from minus infinity to infinity of...

A conditional operator (<exp1>? <exp2>: <exp3>) is called the ternary operator

A symbol that represent a specific action .For example a plus sign (+) is an operator that represent the addition.

Operator of what? Is the real question. I see an operator as someone in charge of whatever it may be.