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1 Dimentional Schrodinger equation

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the one dimensional wave funciton give below.
    a) Draw a graph of the wave function for the region defined.
    b) Determine the value of the normalization constant
    c) what is the probability of finding the particle between x = 0 and x = a/2
    d) show that the wave fucntion is a solution of the non-relativistic wave equation (Schrodinger equation) for the potential energy function give below.
    ψ(x) = A(a^2-x^2) for -a < x < +a
    ψ(x) = 0 for x< -a and x > a
    U(x) = -((h bar)^2/ma^2)(x^2/(a^2-x^2))

    2. Relevant equations
    shown above

    3. The attempt at a solution
    a)
    JK7Qe.png

    b)

    a
    ∫ ψ(x)^2 dx =1
    -a

    a
    ∫ (A(a^2-x^2))^2 dx = 1
    -a

    A = (√15 )/4√a^5

    c)
    39.4%

    d)


    I was given the question without answer, some help verifying my answer would be appreciated!!
     
    Last edited: Oct 14, 2012
  2. jcsd
  3. Oct 14, 2012 #2
    for part d, do I just do this?:
    Meyxo.jpg
     
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