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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 $r=\sqrt{x^2+y^2+z^2}$ 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 wavefunctions, $\psi(r,\theta,\phi)$, which satisfy the time-independent Schrödinger equation (see Sect. 4.12)
H \psi = E \psi,
\end{displaymath} (622)

where the Hamiltonian takes the standard non-relativistic form
H = \frac{p^2}{2 m} + V(r).
\end{displaymath} (623)

Richard Fitzpatrick 2010-07-20