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Homework Help: Wavefunction obeying Schrodinger equation.

  1. May 15, 2010 #1
    1. The problem statement, all variables and given/known data

    I've attached my past paper question, which contains the relevant integral identity too.


    3. The attempt at a solution

    This question is relatively simple, yet I can't seem to complete it.

    I used the schrodinger equation which is:

    -(ħ²/2m)[tex]\nabla^2[/tex]u + Vu = Eu

    I then used the identity given in the question, to differentiate the wavefunction w.r.t to r twice. (In this part I had to differentiate by products since there was another factor of r).

    Differentiating the wavefunction twice gave me:

    (Z²/a²).r.u

    When I put this into the schrodinger equation above, knowing V and E, I dont get the correct answer.
     
    Last edited: May 15, 2010
  2. jcsd
  3. May 15, 2010 #2
    I forgot to say, that it's the first part of the question which I'm having trouble with.


    Thanks.
     

    Attached Files:

  4. May 15, 2010 #3

    Cyosis

    User Avatar
    Homework Helper

    Can't tell you where you go wrong since you barely show any work, but I can tell you two things.

    1) Your Schrodinger equation is incorrect.

    2) You differentiated the wave function twice incorrectly.
     
  5. May 15, 2010 #4
    I've fixed that now. I differentiated the wavefunction using the product rule:

    using the identity given in the question, I had:

    d²/dr²[ r. exp(-Zr/a)] Is this what I need to differentiate?
     
  6. Apr 16, 2011 #5
    Out of interest, how would one go about solving the third part of this question?
     
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