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Homework Help: Wave function of a simple harmonic oscillator

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data
    The ground state wave function of a one-dimensional simple harmonic oscillator is

    [tex]\varphi_0(x) \propto e^(-x^2/x_0^2)[/tex], where [tex]x_0[/tex] is a constant. Given that the wave function of this system at a fixed instant of time is [tex] \phi\phi \propto e^(-x^2/y^2)[/tex] where y is another constant., find the probablity, that if the energy is measured , the system will be in the ground state

    2. Relevant equations

    3. The attempt at a solution

    [tex] dP=|\varphi_0|^2 dx[/tex]

    According to my book(Peebles) , [tex]=|\varphi_0|^2=|\phi_0|^2[/tex];, so therefore [tex] dP=|\phi_0|^2 dx[/tex]?
  2. jcsd
  3. Oct 5, 2009 #2
    anyone still not understand my question?
  4. Oct 6, 2009 #3
    hello noble,
    i'm wondering if you take the integral of your state function from 0 to infinity then divide that result the integral of your ground state function from 0-infinity will you get a function dependent on energy, whereas you could use an energy sample at any time to give the probability?
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