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December 2014 A new approach to the $N$-particle problem in QM
Joachim Schröter
Adv. Theor. Math. Phys. 18(6): 1287-1334 (December 2014).

Abstract

In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic Hamiltonian for arbitrary numbers $N$ of particles by analytical means into a shape such that modern numerical methods can successfully be applied. For this purpose the Cook-Schroeck Formalism is taken as starting point. This includes the use of the occupation number representation. It is shown that the $N$-particle Hamiltonian is determined in a canonical way by a fictional 2-particle Hamiltonian. A special approximation of this 2-particle operator delivers an approximation of the $N$-particle Hamiltonian, which is the orthogonal sum of finite dimensional operators. A complete classification of the matrices of these operators is given. Finally the method presented here is formulated as a work program for practical applications. The connection with other methods for solving the same problem is discussed.

Citation

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Joachim Schröter. "A new approach to the $N$-particle problem in QM." Adv. Theor. Math. Phys. 18 (6) 1287 - 1334, December 2014.

Information

Published: December 2014
First available in Project Euclid: 4 December 2014

zbMATH: 1308.81193
MathSciNet: MR3285610

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 6 • December 2014
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