Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Extensive Wave Function Question

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data
    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 >.

    2. Relevant equations

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

    First excited state (n=2)

    Schrodinger's Equation

    3. 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!
  2. jcsd
  3. Feb 8, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Haven't you already solved the Schrodinger equation for the simple harmonic oscillator? That's normally covered in a QM course.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook