Extensive Wave Function Question

[arp777]

Homework Statement

A particle of mass 'm' moves in a 1-dimensional harmonic oscillator potential. The particle is in the first excited state. Calculate < x >, < x^2 >, < p >, and < p^2 >.

Homework Equations

Harmonic oscillating potential ---> V = (1/2) K x^2

First excited state (n=2)

Schrödinger's Equation

The Attempt at a Solution

I will be alright once I figure out the correct wave function to apply to this scenario. We have a massive particle in a harmonic oscillating potential. This potential is independent of time. Do I simply use a "guess Solution" at ψ(x,t) and have indeterminable constants carried with me throughout this problem? Or is there a way to find a more precise wave function just from the potential that can be used for calculating average position, average momentum, etc..? I have all relevant materials and quantum mechanics text in front of me. Just need some extra light.

Thanks so much!

 

[vela]

Haven't you already solved the Schrödinger equation for the simple harmonic oscillator? That's normally covered in a QM course.