Deformed Heisenberg algebras, a Fock-space representation and the Calogero model

Bardek, V.; Meljanac, Stjepan

doi:10.1007/s100520000457

Cited by 29 publications

(34 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An extension of the method of Section 4 to the N-body Calogero model described in Section 3 leads to time-dependent quasi-exactly-solvable matrix models. Since it is not usual to find exactly solvable or quasi-exactly solvable time-dependent problems, specially in a context of the many-body systems, our results support the program to investigate further time-dependent generalizations of stationary solvable models, like mentioned in the Introduction [2], [3], [4], [6] and quasi-exactly solvable matrix models [28]. In particular, one can focus attention on the dynamical algebras of these models [29] to construct Ermakov-Lewis invariant operators ( [26] and references therein).…”

Section: Discussionsupporting

confidence: 62%

“…Similar considerations hold concerning the intertwining of h (2) ik and h (3) . The "non-quasi-exactly solvable" portions of h (1) ik and h (2) ik coincide [13] because of an additional intertwining between them.…”

Section: Stationary Solutions Of 3-body Problem With Internal Degreesmentioning

confidence: 63%

“…The most widely studied model is the so called Calogero model [1] and its various generalizations which essentially are many-body extensions of the one-dimensional singular harmomic oscillator model. Calogero-like models have been developed incorporating different root systems [2], q-deformations [3], PT-symmetric generalizations [4], many-body forces [5], multi-dimensions [6] and internal degrees of freedom with potentials which couple them (matrix potentials) [7]. Even if coupled channel problems in general have a continuum [8] and discrete spectrum, in the Calogero-like models (with harmonic attraction) the spectrum is purely discrete reflecting an essentially confining dynamics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exactly solvable three-body systems with internal degrees of freedom

Cannata

Ioffe

2001

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body ( and quasi-exactly-solvable N -body ) matrix problems on a line. From intertwining relations with time-dependent operators, we build exactly solvable non-stationary scalar and 2 × 2 matrix 3-body models which are time-dependent extensions of the Calogero model. Finally, we investigate the invariant operators associated to these systems.

show abstract

Section: Discussionsupporting

confidence: 62%

Section: Stationary Solutions Of 3-body Problem With Internal Degreesmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exactly solvable three-body systems with internal degrees of freedom

Cannata

Ioffe

2001

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

“…where the parameter α = √ C + µ is introduced, with C determined by (18). The radial Hamiltonian (51) is shape invariant and this property can be verified by introducing the corresponding superpotential…”

Section: Susyqm Analysis Of the Radial Partmentioning

confidence: 93%

Quantization and conformal properties of a generalized Calogero model

et al. 2007

Self Cite

View full text Add to dashboard Cite

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

“…a) It can easily be shown that the states |n λ can be regarded as the basis for our new Fock space, since the necessary and sufficient conditions mentioned for a onedimensional quantum mechanical Fock space in [Bardek(2000)] will be satisfied. In our problem these conditions are briefly i) existence of a vacuum state such that a|0 = 0,…”

Section: Some Remarkable Pointsmentioning

confidence: 99%

Representations of coherent and squeezed states in af-deformed Fock space

Roknizadeh¹,

Tavassoly²

2004

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Abstract. We establish some of the properties of the states interpolating between number and coherent states denoted by |n λ ; among them are the reproducing of these states by the action of an operator-valued function on |n (the standard Fock space) and the fact that they can be regarded as f -deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.

show abstract

Deformed Heisenberg algebras, a Fock-space representation and the Calogero model

Cited by 29 publications

References 6 publications

Exactly solvable three-body systems with internal degrees of freedom

Exactly solvable three-body systems with internal degrees of freedom

Quantization and conformal properties of a generalized Calogero model

Representations of coherent and squeezed states in af-deformed Fock space

Contact Info

Product

Resources

About