Wavefunction obeying Schrodinger equation.

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Homework Help Overview

The discussion revolves around a problem related to the Schrödinger equation and the differentiation of a wavefunction in the context of quantum mechanics. The original poster is attempting to solve a question from a past paper that involves applying an integral identity and differentiating the wavefunction with respect to the radial coordinate.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to differentiate the wavefunction using the Schrödinger equation and an integral identity but encounters difficulties in achieving the correct answer. Some participants question the correctness of the Schrödinger equation used and the differentiation process. There is also a request for clarification on the differentiation of a specific expression involving the wavefunction.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts. There are indications of missteps in the differentiation process and the formulation of the Schrödinger equation. The original poster has made adjustments based on feedback but continues to seek guidance on specific aspects of the problem.

Contextual Notes

The original poster is focused on the first part of the question and has expressed uncertainty about their approach. There is a mention of a third part of the question, indicating that the discussion may extend beyond the initial problem.

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

Attachments

  • QM question s.jpg
    QM question s.jpg
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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.
 
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?
 
Out of interest, how would one go about solving the third part of this question?
 

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