Students are referred to texts on quantum mechanics for the derivations of the results summarised in this appendix, which is intended as no more than an aide-memoire.

C.1 Orbital angular momentum

In the shell model of both atomic and nuclear physics the single-particle Schrodinger equation, neglecting effects of the intrinsic spin of the particle, is of the form

where the potential energy V(r) is spherically symmetric, a function of the radial coordinate r only. Because of spherical symmetry, the operator ᐁ2 is most useful in spherical polar coordinates (r, θ, ɸ), in which the Schrodinger equation takes the form

where L2 = L2x + L2y + L2z and L is the orbital angular momentum operator,