- #1

- 4

- 0

## Homework Statement

Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic

oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate

the average potential energy <0|[tex]\hat{v}[/tex]|0> and average kinetic energy <0|[tex]\hat{T}[/tex]| 0>

## Homework Equations

[tex]\int^{\infty}_{0}[/tex](x[tex]^{2n}[/tex] e[tex]^{-ax^{2}}[/tex])dx=[tex]\frac{1x3x5x...x(2n-1)}{2^(n+1)a^n}[/tex][tex]\sqrt{\frac{\pi}{a}}[/tex]

## The Attempt at a Solution

I did the ground state harmonic oscillation standard alteration with "a" and got [tex]\\Psi_{0}[/tex](x)=1/([tex]\pi^{1/4}[/tex][tex]\sqrt{x_{0}}[/tex])*e^-x^2/2x[tex]^{2}_{0}[/tex]