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!

Homework Help: Time development wave of state

  1. Nov 1, 2009 #1
    1. The problem statement, all variables and given/known data

    free particle of mass m moving in 1d
    state: [tex]\Psi(x,0) = sin(k_{0}x)[/tex]

    2. Relevant equations

    [tex]\Psi(x,t) = \stackrel{1}{\overline{\sqrt{2\pi}}}\overline{}[/tex][tex]\int^{\infty}_{-\infty}b(k)e^{i(kx-\omega t)} [/tex]

    3. The attempt at a solution

  2. jcsd
  3. Nov 1, 2009 #2


    User Avatar
    Science Advisor
    Gold Member

    The problem here is that you have sine instead of [tex]e^{ikx}[/tex] factor.
    Use the fact that:
    [tex]sin(kx) = \frac{1}{2i}(e^{ikx}-e^{-ikx})[/tex]

    Second your answer should be:
    [tex]\Psi(x,t) = ... [/tex]
    [tex]b(k) = ...[/tex]
    Look up the source of your "relevant equation" to see what role [tex]b(k)[/tex] plays....also you should give the variable of integration which appears to be k.

    Your attempted solution is I suppose integrated over x? The integral you give has a known solution in terms of Dirac delta functions (which relates to my point above)

    Remember ultimately you are looking for a solution to the Schrodinger equation which a.) is properly normalized and b.) satisfies the initial condition given.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook