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About this book. In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable.
- The Cm System
- Additional Results
- Historical Notes
- Acknowledgements
- References
- Recommended Reading
The dynamical system that is generally called Calogero-Moser (hereafter CM) is the model characterized by the Hamiltonian\tag{1}H\left( \underline{p},\underline{q}\right) =\frac{1}{2}\sum_{n=1}^{N}\left(p_{n}^{2}+\omega ^{2}q_{n}^{2}\right) +g^{2}\sum_{m,n=1;m\neq n}^{N}\left(q_{n}-q_{m}\right) ^{-2}~. H(p−,q−)=12∑n=1N(p2n+ω2q2n)+g2∑m,n=1;m≠nN(qn−q...
There are several variations on, and generalizations of, the CM system, and connections with other problems (in addition to those mentioned above). In this section they are outlined quite tersely: the reader whose interest isstimulated by these hints will have no difficulty to pursue the specific matter via the web (possibly also using as guidance ...
The first paper introducing and solving, in a quantal context, the CM system on the line with arbitrary N is [C1971] (for N=3 this problem had been solved a bit earlier [see(C1969)]; the analogous model on the circle – or equivalently with the rational (inverse-square) potential in (1) replaced by the trigonometric (inverse-sine-square) potential, ...
It is a pleasure to thank Mario Bruschi, Jean-Pierre Françoise andMatteo Sommacal for having accepted to be co-curators of this Scholarpediaentry and for helpful feedbacks on this article.
[BC1990] M. Bruschi and F. Calogero: General analytic solution of certain functional equations of addition type, SIAM J. Math. Anal. 21(1990), 1019-1030 [C1969] F. Calogero: Solution of a three-body problemin one dimension, J. Math. Phys. 10 (1969), 2191-2196 [C1971] F. Calogero: Solution of the one-dimensional N-body problem with quadratic and/or ...
Perelomov, A. M. 1990. Integrable systems of classical mechanics and Lie algebras. Birkhauser, Basel.
6 de dic. de 2012 · The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such...
metric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the symmetric monomial superfunctions. Many explicit examples are displayed. Furthermore, various new results have been obtained for the supersymmetric version
16 de jul. de 2001 · Calogero–Moser–Sutherland models. The CMS-models describe systems of N particles interacting pairwise through long-range potentials. The classical and quantum versions of these models are integrable.
20 de nov. de 2002 · PDF | We first review the construction of the supersymmetric extension of the (quantum) Calogero-Moser-Sutherland (CMS) models. We stress the remarkable... | Find, read and cite all the...
The Calogero-Moser model, the Calogero model and the Sutherland model describe quantum integrable particle systems with long-range interactions and have attracted considerable interest. We explicitly give the solution of the Cauchy problem for the two-body problem of each of the Calogero-Moser model and the Calogero model.
