Generalized Pseudo-Potentials for Higher Partial Wave Scattering
R Stock, A Silberfarb, I H. Deutsch, E L. Bolda
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.
Physical Review Letters
Fermi Pseudopotential, harmonic atom trap, partial wave, spectrum
, Silberfarb, A.
, Deutsch, I.
and Bolda, E.
Generalized Pseudo-Potentials for Higher Partial Wave Scattering, Physical Review Letters
(Accessed June 1, 2023)