Chapter 3 Methods

Computational methodology is based on the six, well-established postulates of quantum theory.

Postulate 1: The state (or wave) function, \(\Psi\), describes the state of any quantum mechanical system

Postulate 2: Linear, Hermetian quantum mechanical operators exist which correspond to any physical observable of the system

Postulate 3: The physical observable, \(A\), associated with its corresponding operator, \(\hat{A}\), is the eigenvalue, \(a_i\), of the eigenvalue equation \(\hat{A}\phi_i = a_i\phi_i\)

Postulate 4: The wave function, \(\Psi\), can be expanded into a complete set of eigenfunctions of a linear, Hermetian operator.

Postulate 5: The expectation value, \(\left\langle A \right\rangle\), of the operator, \(\hat{A}\), is the average value of the observable for a normalized wave function at time \(t\).

Postulate 6: The wave function of a system evolves with time as given by the time-dependent Schrödinger equation.