par Quesne, Christiane
Référence Journal of Physics A: Mathematical and General, 21, 24, page (4501-4511), 007
Publication Publié, 1988
Article révisé par les pairs
Résumé : The results of a previous paper (ibid., vol.21 p.4487, 1988), concerned with the first family of two-parameter Poschl-Teller potentials, are used to obtain potential and dynamical potential algebras for the subfamily of one-parameter symmetrical Poschl-Teller potentials. They are respectively identified with so(3) and so(3, 1) algebras, and shown to be subalgebras of the so(4) potential and sl(4, R) dynamical potential algebras of the two-parameter potentials. All the Hamiltonian eigenstates, corresponding to the subfamily of potentials with quantised potential strengths mu differing by an integer, are proved to belong to a single degenerate continuous unitary irreducible representation of so(3, 1), which may be labelled by generalised Young pattern labels ( omega 0), where omega =- 1+1/4i eta , and eta is some real parameter. An sp(4, R) approximately=so(3, 2) algebra is also constructed and shown to provide an alternative choice for the dynamical potential algebra of the symmetrical potentials. All the above-mentioned eigenstates belong to a single sp(4, R) unitary irreducible representation of the positive discrete series, which may be labelled by its lowest weight (1/2 1/2). Such an alternative choice for the dynamical potential algebra, however, does not lead to a unified treatment of the one- and two-parameter potentials as does the first one.