Progress of Theoretical Physics

One-Dimensional Many-Fermion System. I: Exact Solution in a Field Theoretical Framework

T. Kebukawa

Published May 1, 1985• 3 citations

Abstract

The eigenvalue problem in a one-dimensional system of many fermions interacting via a delta-function potential is solved exactly in a field theoretical framework. Simultaneous eigenstates of spin and energy are represented in a systematic and compact form, that is, in such a form that the orbital and spin eigenfunctions are unified in harmony without the aid of Young’s tableau. The eigenstate and energy eigenvalue are specified by two sets of quantum numbers, particle momenta and spin momenta, besides two eigenvalues of a total spin angular momentum and its z-component. It is shown that for given particle momenta and spin momenta the energy eigenvalue is given by the solutions of coupled equations.

DOI: 10.1143/ptp.73.1098

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