Lattice oscillator model, scattering theory and a many-body problem

Manuel Valiente Cifuentes

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Abstract

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in a supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. We then define an operator whose continuum limit corresponds to an angular momentum in terms of the creation-annihilation operators of our model. Coherent states with the correct continuum limit are also constructed. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.

Original languageEnglish
Article number465303
Number of pages9
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number46
DOIs
Publication statusPublished - 26 Oct 2011

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