Chapter 10, Problem 10.72E

Interpretation Introduction

Interpretation:

The reason as to why $\left(1/X\right)\left(d^2/d{x}^2\right)X$ is defined as $\left(-2m{E}_x/{\hslash }^2\right)$ and not simply as $E$ is to be stated.

Concept introduction:

In quantum mechanics, the wavefunction is given by $\Psi$. The wavefunction contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time.

The time-independent Schrödinger equation for a particle in three dimensions is represented as,

$-\frac{{\hslash }^2}{2m}\left(\frac{{\partial }^2}{\partial x^2}+\frac{{\partial }^2}{\partial y^2}+\frac{{\partial }^2}{\partial z^2}\right)\Psi =E\Psi$