Schrodinger Equation

[firewolfsm]

I may just be using the wrong search queries but I can't seem to find the schrodinger equation in its polar form online. I need it in azimuthal form, polar form, and radial form, that is, with the variables separated. I hate to make a thread for this but I'm sure someone either knows them or can send me a valuable link, it would help a lot.

 

[DrPizza]

Like this?
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sch3D.html

 

[firewolfsm]

No, an equation for phi, theta and r separately, I think I may have found it but the constants aren't defined at all (in terms of quantum numbers)

 

[silverpig]

No, an equation for phi, theta and r separately, I think I may have found it but the constants aren't defined at all (in terms of quantum numbers)

The equation is only separable under certain circumstances (ie, point potential).

The Griffiths book has the entire solution for the hydrogen atom. That's probably what you want.

 

[silverpig]

No, an equation for phi, theta and r separately, I think I may have found it but the constants aren't defined at all (in terms of quantum numbers)

Pizza's link had that. If you just want the equation, that's what was there... if you want a particular solution, then you need to specify a potential.

 

[firewolfsm]

My assignment says to consider the azimuthal, polar, and radial schroedinger euqation for a central potential U(r), it's not a particular solution I need but the general differential equation for each parameter. This should be obtained after separation of variables is done on the standard radial equation.

 

[silverpig]

I guess what you want is

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html

bottom of the page.

 

[firewolfsm]

Ah, that is what I wanted, thank you. I never found that in time and actually separated the original equation myself. It should at least help me get a better recommendation out of him.

 

[Farmer]

To get that quickly, just remember the spherical form of the Laplace operator, since that's the only thing special in that form of the Hamiltonian. For a generic (non-central) potential, if it's defined in cartesian coordinates, just convert cartesian to spherical using the old x = r sin(theta) cos(phi), etc.