Exact Wavefunctions for a Delta Function Bose Gas with Higher Derivatives

TL;DR

This paper constructs exact wavefunctions and spectrum equations for a one-dimensional Bose gas with higher derivative kinetic energy and delta interactions, extending understanding of such quantum systems.

Contribution

It introduces a method to derive exact wavefunctions and spectrum equations for bosons with arbitrary derivative order and particle number.

Findings

Exact wavefunctions for arbitrary particles and derivatives

Spectrum equations for eigenvalues derived

Generalization of Bose gas models to higher derivatives

Abstract

A quantum mechanical system describing bosons in one space dimension with a kinetic energy of arbitrary order in derivatives and a delta function interaction is studied. Exact wavefunctions for an arbitrary number of particles and order of derivative are constructed. Also, equations determining the spectrum of eigenvalues are found.