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

Homework Help: Finding the wavefunction

  1. Nov 5, 2006 #1
    In this problem I am given a function [tex] a(k) = \frac{C \alpha}{\sqrt{ \pi}} e^{-\alpha ^2 k^2} [/tex]
    where alpha and C are both constants

    Now I am supposed to construct [tex] \psi (x,t) [/tex]

    My work:
    [tex]\psi (x,t) = \int_{-\inf}^{\inf} a(k) e^{i[kx - \omega (k) t]} dk [/tex]
    pull out the constants from our given function and join exponentials to get
    [tex]\psi (x,t) = \frac{C \alpha}{\sqrt{\pi}} \int_{-inf}^{inf} e^{i[kx - \omega (k) t] - \alpha ^2 k^2} dk [/tex]
    Here's where I am unsure. This is strange integral to evaluate, but my tactic was to complete the square, and hope for the best. The rest of my work is shown below, but I don't know if it is right or not
    [tex]\psi (x,t) = \frac{C \alpha}{\sqrt{\pi}} \int_{-inf}^{inf} e^{-(\alpha k - kx/2)^2 - (kx/2)^2 - \omega (k)t} dk [/tex]
    Where do I go from here? What is the best way to evaluate this integral?
    Last edited: Nov 5, 2006
  2. jcsd
  3. Nov 5, 2006 #2
    Maybe quantum mechanics isn't intro level physics, should this be moved to advanced physics?

    Also, what is the LaTeX command for infinity?
  4. Nov 5, 2006 #3


    User Avatar
    Science Advisor
    Homework Helper

    It probably should be in the advanced section, but it is here now.

    Have you tried expresseing the complex exponential in terms of sine and cosine? Have you tried using an online calculus tool to look up the integral?

    [tex] \infty [/tex]

    Do you have a finctional form for [tex] \omega (k) [/tex]?
    Last edited: Nov 5, 2006
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook