How to Prove a 1D Harmonic Oscillator in Ground State Obeys the HUP?

[pcheminsanity]

Homework Statement

Prove that a 1-d harmonic oscillator in ground state obeys the HUP by computing delta P sub x and delta X

Homework Equations

delta x = sqrt(<x^2>-<x>^2)
delta px = sqrt(<px^2>-<px>^2)

The Attempt at a Solution

I have absolutely no idea where to start with this. Maybe I'm missing something simple (doubtful - I'm a chem major getting crushed by p-chem - very little calc experience), but I have no idea how to do this and it's driving me absolutely nuts. Any help would be great.

 

[turin]

You need:

the 1-D ground-state wave function of the harmonic oscillator.
the definition of expectation value (the angle bracketed objects are expectation values).