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!

One dimensional Schroedinger equation solution

  1. Mar 19, 2013 #1
    1. The problem statement, all variables and given/known data
    before a potential barrier show;
    ψ(x) = B*sin(kx-∅)
    B, k and ∅ are all possitive

    Is a solution of the one dimensional Schroedinger equation
    2. Relevant equations
    ψ(x) = B*sin(kx-∅)
    Eψ(x) = -(ħ2/2m)(d2ψ(x)/dx2)+U(x)ψ(x)

    3. The attempt at a solution
    If it is before the barrier U(x) = 0 so;
    Eψ(x) = -(ħ2/2m)(d2ψ(x)/dx2)

    ψ(x) = B*sin(kx-∅)
    dψ(x)/dx= Bk*cos(kx-∅)
    (d2ψ(x)/dx2) = -Bk2*sin(kx-∅)

    By substitution;
    E = ħ22k2/2m
    λ = h/p (de broglie wavelength)
    p = mv
    h = λmv
    so k = 2π√(2Em) / λmv
    apparently I should get;
    What I have is a multiple of 2π/λ
    What have I done wrong / what else should I do
    Thanks in advance for and help you offer
  2. jcsd
  3. Mar 19, 2013 #2
    E = 0.5 * m * v^2 I got it :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: One dimensional Schroedinger equation solution