Chapter 10, Problem 10.29E

Interpretation Introduction

Interpretation:

The probability that the particle will exist in the first third of the interval, that is, from $x=\text{0}\text{to}\left(1/3\right)a$ and the probability that the particle will be in the third of the box, that is, from $x=\left(2/3\right)a\text{to}a$ are to be stated.

Concept introduction:

For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(N\Psi \right)\left(N{\Psi }^{*}\right)}=1$

Where,

• $N$ is the normalization constant

• ${\Psi }^{*}$ is the conjugate of the wavefunction

• $\Psi$ is the wavefunction