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Spectral characteristics for a spherically confined -a/r+br 2 potential. (English) Zbl 1215.81144
Summary: We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r)=-a/r+br 2 , b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential V(r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the help of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.
MSC:
81V45Applications of quantum theory to atomic physics
81Q05Closed and approximate solutions to quantum-mechanical equations
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
39B12Iterative and composite functional equations
81T80Simulation and numerical modelling (quantum field theory)