A new model of the Calogero type

We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying SU (1, 1) symmetry, we find that the analytic solutions of this model can be described within the scope of the Bargmann representation analysis and we investigate its dynamical structure by constructing the corresponding Fock space realization. The analysis from the standpoint of supersymmetric quantum mechanics (SUSYQM), when applied to this problem, reveals that the model is also shape invariant. For a certain range of the system parameters, the two-body generalization of the Calogero model is shown to admit a one-parameter family of self-adjoint extensions, leading to inequivalent quantizations of the system. PACS number(s): 02.30. Ik, 03.65.Fd,

show abstract

“…[16]. The operators T + , T − , T 0 in (2) are expressed in terms of the polar coordinates x 1 = r sin φ, x 2 = r cos φ.…”

Section: Bargmann Representation Analysismentioning

confidence: 99%

Quantization and conformal properties of a generalized Calogero model

et al. 2007

View full text Add to dashboard Cite

show abstract

“…in which we see that the function V −2 (A − , B − ) gives rise to an homogeneous function of degree −2 in the canonical coordinates. In the N = 2 case (and with a vanishing radial perturbation J ) the quantum mechanical analogue of (2.11) has been studied in [36] as an exactly solvable 'generalization' of the 2D Calogero-Moser model. Therefore, presumably (2.11) provides a good candidate for a new exactly solvable (classical and quantum) model in arbitrary dimension.…”

Section: A New Nd Integrable Modelmentioning

confidence: 99%

Integrable perturbations of the N-dimensional isotropic oscillator

Ballesteros

Blasco

2010

Physics Letters A

View full text Add to dashboard Cite

Two new families of completely integrable perturbations of the N -dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h 6 -coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N − 1) 'Rosochatius' terms that preserve the complete integrability of all these models.

show abstract

“…The early works of Calogero and Sutherland have been extended to many more complex systems, concerning two-and three-body problems. We can quote, in a non exhaustive way, the works of several authors [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Exactly solvable $N$-body quantum systems with $N=3^k \ ( k \geq 2)$ in the $D=1$ dimensional space

Bachkhaznadji,

Lassaut

2016

Preprint

View full text Add to dashboard Cite

We study the exact solutions of a particular class of N confined particles of equal mass, with N = 3 k (k = 2, 3, ...), in the D = 1 dimensional space. The particles are clustered in clusters of 3 particles. The interactions involve a confining mean field, two-body Calogero type of potentials inside the cluster, interactions between the centres of mass of the clusters and finally a non-translationally invariant N-body potential. The case of 9 particles is exactly solved, in a first step, by providing the full eigensolutions and eigenenergies. Extending this procedure, the general case of N particles (N = 3 k , k ≥ 2) is studied in a second step. The exact solutions are obtained via appropriate coordinate transformations and separation of variables. The eigenwave functions and the corresponding energy spectrum are provided.

show abstract

A new model of the Calogero type

Cited by 9 publications

References 13 publications

Quantization and conformal properties of a generalized Calogero model

Quantization and conformal properties of a generalized Calogero model

Integrable perturbations of the N-dimensional isotropic oscillator

Exactly solvable $N$-body quantum systems with $N=3^k \ ( k \geq 2)$ in the $D=1$ dimensional space

Contact Info

Product

Resources

About