Ruibin Zhang (University of Sydney)
Friday 18th May, 12.05-12.55pm, Carslaw 375
Representations of orthogonal and orthosymplectic Lie algebras in the quantum Kepler problemThe quantum Kepler problem is the study of a class of integrable two body quantum systems, the simplest of which is the hydrogen atom. It is shown that the system defined on R^{D} has an so(2, D+1) dynamical symmetry, and that defined on the superspace R^{D|2n} has a dynamical symmetry described by the orthosymplectic Lie superalgebra osp(2, D+1|2n). In each case, the negative energy eigenspaces span an infinite dimensional irreducible highest weight module for the dynamical symmetry algebra. The module is constructed explicitly, and its weight spaces are determined by studying the branching of the module with respect to so(D+1) or osp(D+1|2n). This in turn enables us to work out the spectrum of the quantum Hamiltonian, the corresponding energy eigenspaces and their dimensions. Representation theoretical solutions of generalised Kepler problems with magnetic monopole interactions will also be given. Part of the material in this talk is based on joint work with Guowu Meng. |