Chapter 7, Problem 7.6P

Interpretation Introduction

Interpretation:

The Schrodinger equation for particle of mass m and potential energy varies as ${\text{ax}}^{\text{4}}$ with a constant has to be written.

Concept Introduction:

The wave function or state function of quantum mechanical system is described by using a liner partial differential equation called Schrodinger equation. The respective wave function is used to define the probability of finding the particle at certain position of the system.

The Hamiltonian wave function equals the total energy (kinetic + potential) energy of the system. That is $H\text{ψ}=E\text{ψ}$.

$\begin{array}{l}\underset{\_}{Schrodinger\text{'}sEquation}:\\ -\frac{{\hslash }^2}{2m}\frac{d^2\text{ψ}}{d{x}^2}+V\left(x\right)\text{ψ}=E\text{ψ}\\ here,\\ \hslash =\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$2\pi $}\right.,hisPlanck\text{'}s\text{constant}\\ \psi =wavefunction\\ m=Particlemass\\ V\left(x\right)=Potentialenergy\\ -\frac{{\hslash }^2}{2m}\frac{d^2\text{ψ}}{d{x}^2}=Kineticenergy\end{array}$