Chapter 12, Problem 12.50E

Interpretation Introduction

(a)

Interpretation:

The secular determinant for a system that is described in terms of four ideal wavefunctions is to be stated.

Concept introduction:

Variation theory states that the average energy of any wavefunction for a given system is equal to or greater than its ground-state energy. It provides more accurate value of energy for a particular system. It is used to find the approximate solutions to the Schrödinger equation.

Interpretation Introduction

(b)

Interpretation:

The explanation of the complexity of a secular determinant as the number of ideal wavefunctions increases is to be stated. The number of $H$ and $S$ integrals that are needed to be evaluated is to be predicted.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.