Solving of schrodinger's wave equation

  • #1
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It's the application of Shrodinger wave equation to H-atom and I can't solve the first step. Please help me solve this. I'm not maths student so it's really hard to solve it:(
d^2 psi/dx^2+d^2psi/dy^2+d^2psi/dz^2+8π^2m/h^2(E-V)=0

Where x= rsin(theta)cos(phi)
y=rsin(theta)sin(phi)
z=rcos(theta)
V=-e^2/r

When we convert Cartesian plans into polar planes, we get:

1/r^2 . d/dr(r^2.d(psi)/dr)+1/r^2sin(theta) . d/d(theta) (sin(theta).d(psi)/d(theta))+ 1/r^2sin^2(theta). d^2(psi)/d(phi)^2+8π^2m/h^2(E+e^2/r)(psi)=0
Please explain in easy steps, how to solve this?
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
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Have you tried looking for example derivations online?
i.e.

We can help you with where you get stuck. There are many resources for showing you how to do this.
Basically it involves noticing that you can separate out the radial and angular components, then looking up the form of the resulting DEs (nobody does it from scratch).
 

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