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: Schrodinger equation and free particles

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Show whether the functions
    psi_I = A cos(kx - wt)
    psi_II = A sin(kx - wt)
    are solutions of Schrodinger equation for a free particle

    2. Relevant equations
    Schrodinger equation

    3. The attempt at a solution
    For psi_I = A cos(kx - wt),
    d2psi_I/dx2 = -Ak2psi[/SUB]I[/SUB]
    dpsi_I/dt = Awsin(kx - wt)
    Substituting into S.E,
    ih_bar Awsin(kx - wt) = ((h_bar)2/2m) Ak2psi_I + 0 psi (free particle so V=O)
    So it doesn't satisfy the S.E.

    For psi_II = A sin(kx - wt),
    d2psi_II/dx2 = -Ak2psi[/SUB]II[/SUB]
    dpsi_II/dt = -Awcos(kx - wt)
    Substituting into S.E,
    ih_bar -Awcos(kx - wt) = ((h_bar)2/2m) Ak2psi_II + 0 psi
    So it doesn't satisfy the S.E either.

    Is this correct? Or is there some way that I'm supposed to manipulate both sides to equal each other? :S
  2. jcsd
  3. Mar 19, 2009 #2


    User Avatar
    Homework Helper

    hi kehler

    as you've shown, they will not be a solution of the Time Independent SE for a free particle by themselves...

    How about a linear combination of the 2 states? ie
    [tex] \psi = C\psi_1 + D\psi_2 [/tex]

    what do C & D have to staisfy to be a solution...?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook