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=(x2+y2+z2)1/2 is the radial distance from the origin. It is, of course, most convenient to work in spherical coordinates—r, θ, ϕ—during such an investigation. (See Section [s8.3].) Thus, we shall be searching for stationary wavefunctions, ψ(r,θ,ϕ), that satisfy the time-independent Schrödinger equation (see Section [sstat]) Hψ=Eψ,
where the Hamiltonian takes the standard non-relativistic form H=p22m+V(r).