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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

    vela

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