Introduction

In this section, 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 $r=\sqrt{x^2+y^2+z^2}$ is the radial distance from the origin. It is, of course, most convenient to work in spherical polar coordinates--$r$, $\theta$, $\phi$--during such an investigation (see Sect. 8.3). Thus, we shall be searching for stationary wave-functions, $\psi(r,\theta,\phi)$, which satisfy the time-independent Schrödinger equation (see Sect. 4.12)

$$H\,\psi = E\,\psi,$$ (601)

where the Hamiltonian takes the standard non-relativistic form

$$H = \frac{p^2}{2\,m} + V(r).$$ (602)