Schrodinger Equation in 3 dimension

[sciboudy]

How can i solve Schrödinger equation in 3dimension i want to know how can i deduce every equation ? and how can i find equation of spherical harmonic and radial equation ?
i need to understand this proof

 

[sciboudy]

i know it's so hard

 

[fzero]

Any decent quantum mechanics text explains how to separate Schrödinger's equation into a radial and angular part when the potential is spherically symmetric. If there's some specific step that is challenging you, please post about it.

For an arbitrary potential, there is no reason to expect a closed-form solution to the radial equation to exist, so it's impossible to answer your question. There are some online resources about ordinary differential equations listed in https://www.physicsforums.com/showthread.php?t=110274&highlight=differential+equations