1. Limited time only! Sign up for a free 30min personal 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!

Finding psi(x,t) using psi(x)

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the free-particle wavefunction,
    ψ(x)=(pi/a)^(-1/4)*exp(-ax^2/2)
    
    Find ψ(x,t)


    3. The attempt at a solution

    The wavefunction is already normalized, so the next thing to find is coefficient expansion function (θ(k)), where:

    θ(k)=∫dx*ψ(x)*exp(-ikx) from -infinity to infinity

    But this equation seems to be impossible to solve without error function (as maple 16 tells me).

    Is there any trick to solve this?
     
  2. jcsd
  3. Sep 20, 2012 #2
    The error function has very nice properties at the infinity, so you should be able to compute the integral. Alternatively, you could use the apparatus of complex analysis to evaluate the integral.
     
  4. Sep 21, 2012 #3
    Why not use some of the simple Gaussian integral tricks (like completing the square in the exponential)? Or am I missing something?
     
  5. Sep 22, 2012 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You can avoid the error function because of the limits on the integral, or equivalently, use the nice properties of the error function at those limits.

    You should really learn to crank this integral out by hand, though. The techniques used are useful to know.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding psi(x,t) using psi(x)
  1. Calculate |Psi(x,t)|^2 (Replies: 2)

Loading...