Chapter 7, Problem 7E.9P

(a)

Interpretation Introduction

Interpretation:

The second derivative on substituting $\psi ={\text{e}}^{-g{x}^2}$ in the equation of harmonic oscillator is to be stated.

Concept introduction:

A harmonic oscillator consists of a particle of mass $m$ that undergoes a restoring force which is proportional to its amplitude $x$.  The restoring force is represented by $k_{\text{f}}$ which is known as the force constant.  The vibrational frequency is $\omega$.  It is directly proportional to the force constant.

(b)

Interpretation Introduction

Interpretation:

The required form of $g$ and energy have to be stated.

Concept introduction:

The same concept introduction as discussed in part (a).

(c)

Interpretation Introduction

Interpretation:

The compare the equation and energy obtained with the energy of a simple harmonic oscillator.

Concept introduction:

The same concept introduction as discussed in part (a).