Chapter 10, Problem 10.95E

Interpretation Introduction

Interpretation:

The wave function product ${\Psi }_3^{\ast }{\Psi }_4$ over all space for the $\text{1-D}$ particle-in-a-box is to be integrated numerically. The two wave functions for the $\text{1-D}$ particle-in-a-box are orthogonal to each other are to be shown.

Concept introduction:

For the orthogonality of 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.

${\displaystyle \underset{0}{\overset{\infty }{\int }}{\Psi }_m{\Psi }_n}=0$

Where, ${\Psi }_m$and ${\Psi }_n$ are two different wave functions. The essential condition for two wave functions to be orthogonal to each other is $m\ne n$.