The Postulate for Constructing Operators

Postulate II To every observable dynamical variable M there can be assigned a linear hermitian operator M. One begins by writing the classical expression, as fully as possible in terms of momenta and positions. Then  

The reason for specifying that M must be hermitian is that the eigenvalues of a hermitian operator must be real numbers. We shall discuss this and other aspects of hermiticity (including its definition) later in this chapter. 

As an explicit example of this procedure, we reconsider the hydrogen atom. Assuming a fixed nucleus (infinite inertia), the classical expression for the total energy of the system is 

We have discussed only cases where neither the hamiltonian H nor is time dependent. In those cases we required that i/ be an eigenfunction of H. In the more general case in which vT and are time dependent, a different requirement is imposed by 

Postulate III The state functions (or wavefunctions) satisfy the equation 

---