ART OR SCIENCE - THE DETERMINATION OF THE SYMMETRY LIE-ALGEBRA FOR A HAMILTONIAN WITH ACCIDENTAL DEGENERACY

The purpose of this paper is to show that the determination of the symmetry Lie algebra of a Hamiltonian with accidental degeneracy is more a matter of art than science, in the usual sense of these two words. Our thesis is defended through examples in which the Hamiltonians are linear combinations of the number operator N and the angular momentum M of a two dimensional oscillator. The standard approach to the problem when H = N or M, fails for H = N ± M or H = N ± |M|. We develop an alternative analysis for the latter Hamiltonians, which accounts for all the properties that we demand for a symmetry Lie algebra. We show, in the concluding section, examples in which our technique can be applied to more general problems. © 1990.