Chapter 9, Problem 9A.7BE

Interpretation Introduction

Interpretation:

The linear combinations $h_1=\left(\sin \zeta \right)\text{s}+\left(\cos \zeta \right)\text{p}$ and $h_2=\left(\cos \zeta \right)\text{s}-\left(\sin \zeta \right)\text{p}$ are mutually orthogonal for all value of the angle $\zeta$ has to be shown.

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.

  ${\displaystyle \underset{0}{\overset{\infty }{\int }}{\psi }_m{\psi }_n}d\tau =0$

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 $m\ne n$.