In three space dimensions, when a physical system possesses spherical
symmetry, the dynamical equations automatically lead to the Legendre and the
associated Legendre equations, with the respective orthogonal polynomials as
their standard solutions. This is a very general and important result and
appears in many problems in physics (for example, the multipole expansion etc).
We study these equations from an operator point of view, much like the harmonic
oscillator, and show that there is an underlying shape invariance symmetry in
these systems responsible for their solubility. We bring out various
interesting features resulting from this analysis from the shape invariance
point of view.Comment: 4 pages, 1 figure; to appear in PL