Chapter 7, Problem 7D.2DQ

Interpretation Introduction

Interpretation:

The features of solution of particle in a one-dimensional box that are also observed in solutions of particle in two and three dimensional boxes have to be stated.  The feature that occurs in two and three dimensional boxes but not in a one-dimensional box has to be stated.

Concept introduction:

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

  ${\Psi }_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}$

Where,

• $n$ is the number of energy level.
• $a$ 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.