Ground-State Energy of a Mixture of Fermions and Bosons in One Dimension with a Repulsive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>δ</mml:mi></mml:math>-Function Interaction

Abstract

The ground-state energy of a mixture of spin-\textonehalf{} fermions and bosons in one dimension, interacting with a repulsive $\ensuremath{\delta}$-function potential, is analyzed. The wave function is given by repeated use of a generalized Bethe hypothesis. The "momenta" in the hypothesis are determined by coupled Fredholm integral equations. Numerical solutions are given. No phase separation is found.