Abstract
An sl(4,R) dynamical potential algebra, containing the so(4) potential algebra, is constructed for the two-parameter Poschl-Teller potentials of the first kind. For this purpose, the relation between the Wigner rotation matrices and the solutions of the first Poschl-Teller equation is used. Explicit expressions are given for the sl(4,R) generators, as well as for their action on the normalised solutions. All the Hamiltonian eigenstates, corresponding to the family of potentials with quantised potential strengths (m', m) differing by integers, are proved to belong to a single sl(4,R) unitary irreducible representation of the ladder series. For integral values of m' and m, the latter is Dladd(0,0; eta ), while, for half-integral values, it is Dladd(1/2, 1/2; eta ), where eta is some real parameter. Both irreducible representations are also shown to be characterised by generalised Young pattern labels (pqr0), where p=2-1/2i eta , and q=r=0.
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