The “central potenial” problem (example: Hydrogen Atom). This is a potential defined by a radius from a central point, and only by the radius: V(radius)
The “central potenial” problem (example: Hydrogen Atom). This is a potential defined by a radius from a central point, and only by the radius: V(radius)
The most interesting aspect is the dependence of of the wavefunction under rotations in space, so we look at that first.
Try separation of variables in terms of radius r, longitude (“azimuth”) ?, and latitude (“polar angle”) ? and plug into S. equation in these variables: