Particle in a Spherically Symmetric Potential

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In its quantum mechanical formulation, it amounts to solving the Schrödinger equation with the potential V(r) which depend only on r, the modulus of r. Due to the spherical symmetry of the system it is useful to use spherical coordinates r, and . When this is done, the time-independent Schrödinger equation for the system is separable.We outline the solutions in these cases, which should be compared to their counterparts in cartesian coordinates, cf. particle in a box. This article relies heavily on Bessel functions and Laguerre polynomials.