Chapter 7, Problem 7D.5BE

(i)

Interpretation Introduction

Interpretation:

The probability of finding a particle between $0.65L$ and $0.67L$ in a box of length $L$ for ${\psi }_1$ has to be calculated.

Concept introduction:

The wavefunction for particle in a box is given by the expression as follows.

  $\psi (x)=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L}$

Where,

• $n$ is the number of energy level.
• $L$ is the width of the box.

The probability for particle in a box is taken as the square of the wavefunction and is denoted by ${\psi }^2$.  For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits.

(ii)

Interpretation Introduction

Interpretation:

The probability of finding a particle between  $0.65L$ and $0.67L$ in a box of length $L$ for ${\psi }_1$ has to be calculated.

Concept introduction:

The wavefunction for particle in a box is given by the expression as follows.

  $\psi (x)=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L}$

Where,

• $n$ is the number of energy level.
• $L$ is the width of the box.

The probability for particle in a box is taken as the square of the wavefunction and is denoted by ${\psi }^2$.  For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits.