Generalized Pseudopotentials for Higher Partial Wave Scattering

Details Generalized Pseudopotentials for Higher Partial Wave Scattering Generalized Pseudopotentials for Higher Partial Wave Scattering

2004-05-25

arxiv.org/abs/quant-ph/0405153v3

Phys. Rev. Lett. 94, 023202 (2005)

Physics

Quantum Physics

RevTeX 4 pages, 1 figure, final published version

Scientific paper

10.1103/PhysRevLett.94.023202

We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger 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 pseudopotential for s-wave scattering. By 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.

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