# Schrodinger Equation

1. Aug 22, 2011

### KingBigness

1. The problem statement, all variables and given/known data

See attached photo

3. The attempt at a solution

So I have no idea if I have even started this problem correctly so any help would be nice.

My working is set out in one of the pictures.

Any help would be appreciated I really am not quite sure what to do. Can't figure out where the x^2-y^2 comes from.

Thank you!

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2. Aug 23, 2011

### tiny-tim

Hi KingBigness!
I'm guessing really, since this isn't my field , but if you replace r2sin2θcos2φ by r2sin2θ(cos2φ - sin2φ), that looks like x2 - y2

3. Aug 23, 2011

### vela

Staff Emeritus
Leave the r2 alone for now and use the fact that$$\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}$$to get rid of the complex exponentials.

4. Aug 23, 2011

### KingBigness

Thank you both for that, I shall try that and let you know how I go

5. Aug 25, 2011

### KingBigness

Ok I tried that and out came the x^2-y^2

Thank you for that tip.

This is the answer I have ended up with can you let me know if it is correct or if I need to simplify it more? not really sure when to stop =\

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6. Aug 25, 2011

### KingBigness

I lied above....I brought the sin theta squared in before I converted which got rid of the sin theta squared in the final answer.

Is this now correct?

7. Aug 25, 2011

### vela

Staff Emeritus
Yes, that's right, because in spherical coordinates x = r sin θ cos φ and y = r sin θ sin φ.

8. Aug 25, 2011

### KingBigness

Sweet finally got this question complete!

Thank you. Will double check all my algebra later to make sure I haven't done a silly mistake.

Thanks again for your help

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