Chapter 7, Problem 7D.4BE

Interpretation Introduction

Interpretation:

The given functions, ${\psi }_1$ and ${\psi }_3$ are mutually orthogonal has to be proved.

Concept introduction:

For the orthogonality of the two different wave functions, the product of the wave functions is integrated over the entire limits.  It is expressed by the equation as given below.

  ${\displaystyle \underset{0}{\overset{\infty }{\int }}{\psi }^{\ast }{}_i{\psi }_j\text{d}\tau }=0$

Where, ${\psi }_i$ and ${\psi }_j$ are two different wave functions.  The essential condition for two wave functions to be orthogonal to each other is $i\ne j$.