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調和トラップ中の1次元ボース系の理論(5)

正人 大矢

Published Nov 29, 2010• 0 citations
OpenAlex

Abstract

We consider a one-dimensional system of δ-interacting bosons trapped in harmonic potential. For the repulsive and attractive interaction, we derive expressions of ground-state wave functions, excited-state wavefunctions and their energe eigenvaluess of two-body systems.

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The problem of N bosons interacting with each other via repulsive delta-function interactions and with an external, attractive, delta-function potential is solved, within the Hartree approximation, exactly. If the interparticle interactions are above a certain value, there is no bound state. Thus the bound state does not just expand to compensate for the increase in the repulsive Hartree potential. Moreover as the interaction strength is increased to that value, the ground-state wavefunction develops a pole at the position of the attractive potential.
A one-dimensional system consisting of equal numbers of two types of bosons undergoing interactions through delta function potentials is examined. All particles have the same mass but each boson carries a "charge" that distinguishes one boson type from the other. The interactions are such that like particles repel and unlike attract. The amount of attraction and/or repulsion is determined by two adjustable parameters so that the amount of repulsion is not necessary equal to that of attraction.