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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;
    k=2π/λ
    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 :)
     
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