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PUBLICATIONS

Generalized Pseudo-Potentials for Higher Partial Wave Scattering

Published

Author(s)

R Stock, A Silberfarb, I H. Deutsch, E L. Bolda

Abstract

We derive a generalized zero-range pseudo-potential applicable to all partial wave solutions to the Schrodinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher order multipole moments not accounted for with a monopolar delta-function at the origin, as used in the familiar Fermi pseudo-potential for s-wave scattering. By further making the strength of the potential energy-dependent, we derive self-consistent solutions for the entire energy spectrum of the realistic potential. We apply this to study two particles in an isotropic harmonic trap interacting through a central potential and derive analytic expressions for the energy eigenstates and eigenvalues.
Citation
Physical Review Letters
Pub Type
Journals

Keywords

Fermi Pseudopotential, harmonic atom trap, partial wave, spectrum

Citation

Stock, R. , Silberfarb, A. , Deutsch, I. and Bolda, E. (2021), Generalized Pseudo-Potentials for Higher Partial Wave Scattering, Physical Review Letters (Accessed April 16, 2024)

Created October 12, 2021