Scattering and bound states for a class of non-central potentials

Abstract

We obtain L2-series solutions of the nonrelativistic three-dimensional wave equation for a large class of non-central potentials that includes, as special cases, the Aharonov-Bohm, Hartmann, and magnetic monopole potentials. It also includes contributions from the potential term, cos(theta)/r^2 (in spherical coordinates). The solutions obtained are for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The L2 bases of the solution space are chosen such that the matrix representation of the wave operator is tridiagonal. The expansion coefficients of the radial and angular components of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations resulting from the matrix wave equation.

20 pages, 1 figure

References in corpus (4)

• An extended class of L2-series solutions of the wave equation
• L2 series solution of the relativistic Dirac-Morse problem for all energies
• Exact L2 series solution of the Dirac-Coulomb problem for all energies
• L2 series solutions of the Dirac equation for power-law potentials at rest mass energy

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