The second derivative of a delta-function potential: An exactly solvable model

Ilaria Cacciari, Paolo Moretti

Murray T. Batchelor, X-W Guan, A Kundu

We propose an exactly solvable model of one-dimensional anyons with competing δ-function and derivative δ-function interaction potentials. The Bethe ansatz equations are derived in terms of the N -particle sector for the quantum anyonic field model of the generalized derivative nonlinear Schrödinger equation. This more general anyon model exhibits richer physics than that of the recently studied one-dimensional model of δ-function interacting anyons. We show that the anyonic signature is inextricably related to the velocities of the colliding particles and the pairwise dynamical interaction between particles.

D. Villarroel

A study of the discrete spectra of the Schrödinger and Dirac equations for the delta-shell potential in momentum space is presented in this paper. As a general rule, the spectra for exactly solvable potentials are more easily obtained in position space than in momentum space. The delta-shell potential is unique, since its treatment is simpler in momentum space than in position space. This simplicity derives from two facts; firstly, the kernels of the integral equations in momentum space turn into the product of two independent functions, and secondly, no explicit analysis of the boundary condition for the wavefunction is necessary at .

Brian P. Anderson

L. R. Dodd

The Faddeev equations for the one-dimensional system consisting of three identical particles interacting through δ-function potentials are shown to be exactly solvable. The scattering solutions in the form of half-off-shell rearrangement and elastic amplitudes are constructed explicitly and the ground state of the system is derived.

Б.В. Медведев, M. K. Polivanov