Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies

Abstract

Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. Analysis of resonance energies and bound states spectrum is performed using the complex scaling method, where we show their trajectories in the complex energy plane and demonstrate the remarkable fact that bound states cross over into resonance states by varying the potential parameters.

8 pages, 2 tables, 1 figure. 2 mpg videos and 1 pdf table file are available upon request from the corresponding Author

References in corpus (5)

• Reentrant transitions in colloidal or dusty plasma bilayers
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• An extended class of L2-series solutions of the wave equation
• Pade approximation of the S-matrix as a way of locating quantum resonances and bound states
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• Solving for three-dimensional central potentials using matrix mechanics
• Energy spectrum for a short-range 1/r singular potential with a non-orbital barrier using the asymptotic iteration method
• Bound states of a quartic and sextic inverse-powerlaw potential for all angular momenta
• Energy spectrum of a generalized Scarf potential using the Asymptotic Iteration Method and the Tridiagonal Representation Approach
• J-matrix method of scattering for inverse-square singular potential with supercritical coupling I. Theory
• Approximate analytical solutions of the Dirac equation for Yukawa potential plus Tensor Interaction with any $\kappa$-value