Quantum States of Interacting Atoms in Quasi-One-Dimensional Ultracold Trapped Gases

Abstract

We theoretically investigate the quantum states of a Hamiltonian model for quasi-one-dimensional ultracold trapped gases. From the ansatz given by the numerical solution of the Schr ö dinger equation of the system, we develop a scattering potential functional form and an approximate solution for the analytical approach of the model. We obtain the set of approximate eigenstates and eigenenergies that can be used in future improvements on the study of atomic scattering in low dimensional ultracold gases. We also show that there is a parity inversion of the ground state of the model as the interaction strength increases.