8: Path Integrals in Spherical Coordinates

Many physical systems possess rotational symmetry. In operator quantum mechanics, this property is of great help in finding wave functions and energies of a system. If a rotationally symmetric Schrödinger equation is transformed to spherical coordinates, it separates into a radial and several angular differential equations. The latter are universal and have well-known solutions. Only the radial equation contains specific information on the dynamics of the system. Being an ordinary one-dimensional Schrödinger equation, it can be solved with the usual techniques…