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Analysis of the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The repulsive delta-function interaction model in one dimension is reviewed for spinless particles and for spin-1/2 fermions. The problem of solving the differential equation related to the Schrödinger equation is reduced by the Bethe ansatz to a system of algebraic equations. The delta-function interaction is shown to have no effect on spinless fermions which therefore behave like free fermions, in agreement with Pauli's exclusion principle. The ground-state problem of spinless bosons is reduced to an inhomogeneous Fredholm equation of the second kind. In the limit of impenetrable interactions, the spinless bosons are shown to have the energy spectrum of free fermions. The model for spin-1/2 fermions is reduced by the Bethe ansatz to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group of N elements. For some R's this eigenvalue problem itself is solved by a generalized Bethe ansatz. The ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation.

Place, publisher, year, edition, pages
2014. , 28 p.
Series
TVE, 14 025 juni
Keyword [en]
Many-body problem, Bethe ansatz, delta-function interaction, Bethe-Yang ansatz, Gaudin-Yang model, Lieb-Liniger model
National Category
Subatomic Physics
Identifiers
URN: urn:nbn:se:uu:diva-226119OAI: oai:DiVA.org:uu-226119DiVA: diva2:724062
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2014-06-23 Created: 2014-06-12 Last updated: 2014-06-23Bibliographically approved

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CiteExportLink to record
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