SINGLE-VARIABLE REALIZATION OF THE SU(1,1) SPECTRUM GENERATING ALGEBRA AND DISCRETE EIGENVALUE SPECTRA OF A CLASS OF POTENTIALS

A wide range of operators can be expressed in terms of the generators of the SU(1,1) algebra, the spectral properties of which are well known. The authors attempt to find a realisation of the algebra in its most general form and thus evolve a unified approach to the problem of finding the spectra of Hamiltonians amenable to the technique rather than taking each case separately. They extend the analysis to obtain the spectra of potentials whose coordinate dependence is implicit.