Chapter 10, Problem 10.87E

Interpretation Introduction

Interpretation:

The given integrals of the wavefunctions for the $\text{1-D}$ particle-in-a-box are to be verified.

Concept introduction:

For the orthogonality of the two different wavefunctions, the product of the wavefunctions 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 wavefunctions. The essential condition for two wavefunctions to be orthogonal to each other is $m\ne n$.