Homework Help: Wavefunction obeying Schrodinger equation.

1. May 15, 2010

hhhmortal

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)$$\nabla^2$$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. May 15, 2010

hhhmortal

I forgot to say, that it's the first part of the question which I'm having trouble with.

Thanks.

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• QM question s.jpg
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3. May 15, 2010

Cyosis

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.

4. May 15, 2010

hhhmortal

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?

5. Apr 16, 2011

DoubleHelix

Out of interest, how would one go about solving the third part of this question?