- #1

bmb2009

- 90

- 0

## Homework Statement

A particle of mass m is in a potential of V(x) = Kx

^{4}and the wave function is given as ψ(x)= e^-(ax

^{2}) use the variational principle to estimate the ground state energy.

Part B:

The true ground state energy wave function for this potential is a symmetric function of x i.e. ψ

_{0}(x)=ψ

_{0}(-x). Use the result that <ψ

_{0}lψ(β)> = 0 along with an approximately chosen wave function, to estimate the energy of the first excited state.

## Homework Equations

## The Attempt at a Solution

Ok so I know how to compute variational method approximations and I have proven the identity <ψ

_{0}lψ(β)> = 0 earlier on my assignment and understand the identity as well. What I don't understand is the part that says "Use the result that <ψ

_{0}lψ(β)> = 0 along with an approximately chosen wave function, to estimate the energy of the first excited state."

Again I know that when <ψ

_{0}lψ(β)> = 0 the variational principle becomes E

_{1}≤ <ψlHlψ>/<ψlψ> but does the problem want me to chose a different wavefunction? And if so how to I go about choosing this new wave-function?