8: Central Potentials
( \newcommand{\kernel}{\mathrm{null}\,}\)
In this chapter, we shall investigate the interaction of a non-relativistic particle of mass m and energy E with various so-called central potentials, V(r), where r=(x^{\,2}+y^{\,2}+z^{\,2})^{1/2} is the radial distance from the origin. It is, of course, most convenient to work in spherical coordinates—r, \theta, \phi—during such an investigation. (See Section [s8.3].) Thus, we shall be searching for stationary wavefunctions, \psi(r,\theta,\phi), that satisfy the time-independent Schrödinger equation (see Section [sstat]) \label{e9.1} H\,\psi = E\,\psi, where the Hamiltonian takes the standard non-relativistic form \label{e9.2} H = \frac{p^{\,2}}{2\,m} + V(r).
