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Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
Abstract
The repulsive $\ensuremath{\delta}$ interaction problem in one dimension for $N$ particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations $R$ of the permutation group ${S}_{N}$. For some $R'\mathrm{s}$ this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-\textonehalf{} fermions is reduced to a generalized Fredholm equation.
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Citations
Cites
Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
Bethe, H. (1931) · Zeitschrift f�r Physik · doi:10.1007/bf01341708 · Cited by 3,768
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Bloch, I., Dalibard, J., & Zwerger, W. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.885 · Cited by 8,114
Quantum integrable systems related to lie algebras
Olshanetsky, M. A., & Perelomov, A. M. (1983) · Physics Reports · doi:10.1016/0370-1573(83)90018-2 · Cited by 991
Spin-imbalance in a one-dimensional Fermi gas
Liao, Y.-A., Rittner, A. S. C., Paprotta, T., Li, W., Partridge, G. B., Hulet, R. G., Baur, S. K., & Mueller, E. J. (2010) · Nature · doi:10.1038/nature09393 · Cited by 532
Grassmannian Geometry of Scattering Amplitudes
Arkani-Hamed, N., Bourjaily, J., Cachazo, F., Goncharov, A., Postnikov, A., & Trnka, J. (2016) · Cambridge University Press eBooks · doi:10.1017/cbo9781316091548 · Cited by 432
Gaudin, M. (2014) · Cambridge University Press eBooks · doi:10.1017/cbo9781107053885 · Cited by 290
Metadata
- Authors
- Yang, C. N.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1967-12-04
- Volume
- 19
- Issue
- 23
- Pages
- 1312-1315
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2052372389
- Cited by
- 2,402
- References
- 1
- FWCI
- 3.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- Yang, C. N. (1967). Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction. Physical Review Letters. https://doi.org/10.1103/physrevlett.19.1312
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