Wavefunction obeying Schrodinger equation.

[hhhmortal]

Homework Statement

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

The Attempt at a Solution

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

I used the Schrödinger equation which is:

-(ħ²/2m)\nabla^2u + 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 Schrödinger equation above, knowing V and E, I don't get the correct answer.

 

[hhhmortal]

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

 

[Cyosis]

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

1) Your Schrödinger equation is incorrect.

2) You differentiated the wave function twice incorrectly.

 

[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?

 

[DoubleHelix]

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