Chapter 10, Problem 10.85E

Interpretation Introduction

Interpretation:

The validation of the given statement that wavefunctions, ${\Psi }_{111}$ and ${\Psi }_{112}$ for the $\text{3-D}$ particle-in-a-box is orthogonal to each other is to be shown.

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 $m\ne n$.