Schrodinger Equation in Spherical co-ordinates. Constants.

[rwooduk]

When normalising the S.E. in spherical coordinates you split it up into 3 integrals, with respect to r, theta and phi.

My question is, once you have found the constants for each, when writing out the normalised PSI do you simply place them as a product in the solution?

i..e PSI (r,theta,phi) = ABC r exp (-r/2a) cos (theta)

where ABC are the normalised constants from each part?

Thanks again for any help!

 

[vanhees71]

That's correct, because you just choose the overall constant such that the wave function is normalized in the sense of the Hilbert-space norm. What you have written down is the [itex]n=2[/itex], [itex]l=1[/itex], [itex]m=0[/itex] hydrogen wavefunction,

https://en.wikipedia.org/wiki/Hydro...chr.C3.B6dinger_equation:_Overview_of_results

 

[rwooduk]

That's correct, because you just choose the overall constant such that the wave function is normalized in the sense of the Hilbert-space norm. What you have written down is the [itex]n=2[/itex], [itex]l=1[/itex], [itex]m=0[/itex] hydrogen wavefunction,

https://en.wikipedia.org/wiki/Hydro...chr.C3.B6dinger_equation:_Overview_of_results

Excellent. Thank you!