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Progress of Theoretical Physics

Reduced Model of Anderson-Hamiltonian. II: Exact Spin Eigenstates

T. Kebukawa

Published Jan 1, 1986• 0 citations
Publisher

Abstract

It is shown that the energy eigenstate of the reduced model of Anderson-Hamiltonian proposed in a prewious paper1) is simultaneously the spin eigenstate. M parameters (M denotes the number of down spin electrons) are introduced in the representation of the coupled equations of which solutions give the energy eigenvalue. Two notes on the solution of the eigenvalue problem are presented.

DOI
10.1143/ptp.75.27

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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.
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