1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time Dependant One Dimensional Square well

  1. Apr 2, 2012 #1
    Given the wave function: Ψtot(x,t) = ((√2)/2)ψ3e^(-(iE3t)/[STRIKE]h[/STRIKE]) + ((√2)/2)ψ5e^(-(iE5t)/[STRIKE]h[/STRIKE]) @ |x|≤a/2 and ψtot(x,t) = 0 @ |x|≥a/2 where a=100nm , E=((([STRIKE]h[/STRIKE])^2)((kn)^2))/2m , kn=pi*n/a , & T1 = 2pi[STRIKE]h[/STRIKE]/E1

    How would I find the Period of the wave function in terms of T1??
     
  2. jcsd
  3. Apr 4, 2012 #2

    collinsmark

    User Avatar
    Homework Helper
    Gold Member

    Hello JPurdie7,

    Welcome to physics forums!

    I take it you mean the time period of the expectation value of the wavefunction with respect to T1?

    Hypothetically, you could calculate the expectation value of the wavefunction
    [tex] \int_{x=- \infty} ^{\infty} \Psi^*(x, t) x \Psi(x, t) dx, [/tex]
    but you probably don't need to actually fully evaluate the integral, if you keep an eye on the math.

    But go ahead and evaluate the integrand. Keep an eye on terms that are only a function of t that you can pull out from under the integral. [Edit: you'll need to do a bit of multiplication first, but no integration.]

    And keep the exponential representations of sine and cosine in your back pocket. They might come in handy, if you recognize them.

    Edit: Just in case, for your reference:

    [tex] \sin(\omega t) = \frac{e^{i \omega t} - e^{-i \omega t}}{2i} [/tex]

    [tex] \cos(\omega t) = \frac{e^{i \omega t} + e^{-i \omega t}}{2} [/tex]
     
    Last edited: Apr 4, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook