Factorizations of one-dimensional classical systems

Kuru, Ş.; Negro, J.

doi:10.1016/j.aop.2007.10.004

Cited by 59 publications

(95 citation statements)

References 11 publications

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“…For this we shall mainly follow the factorization technique of ref. [1]. We assume a factorization of the Hamiltonian H in the form…”

Section: Formalismmentioning

confidence: 99%

“…al. obtained exact solutions of the classical analogues of some exactly solvable one-dimensional quantum mechanical models in the framework of the factorization technique [1]. However, it must be kept in mind that this method cannot be applied to all classical systems as not all quantum mechanical models have exactly solvable classical analogues.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, its classical analogue can be solved exactly by means of the interesting factorization method developed in ref. [1]. Our aim here is to see if the above system contains periodic or irregular trajectories, and check if the spontaneous breakdown of PT symmetry switching energy from real values to complex conjugate pairs, manifests itself in the corresponding classical system as well, in terms of non-periodicity of orbits or any other feature.…”

Section: Introductionmentioning

confidence: 99%

“…To make the paper self contained, in Section 2 we briefly discuss the factorization technique of ref. [1] to obtain the classical trajectories of some exactly solvable one dimensional systems, and extend the same to complex classical systems. Based on the equations obtained in Section 2, in Section 3 we obtain the equations of the classical trajectories, the classical momenta and the phase-space trajectories of a particle under the influence of the complex Scarf II potential, and plot the corresponding figures for different values of the coupling parameterv 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by these studies, in this work we intend to extend the factorization technique of ref. [1] to study complex classical systems, which are classical analogues of non Hermitian quantum mechanical systems. In particular, we shall apply the technique to study the classical analogue of the following exactly solvable quantum mechanical PT symmetric (complex) Scarf II potential [9] V (x) = −v 1 sech 2 x −v 1 sech x tanh x ;…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Study of classical mechanical systems with complex potentials

Sinha¹,

Dutta²,

Roy³

2011

Physics Letters A

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We apply the factorization technique developed by Kuru et. al. [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature -the closed orbits become open ones.

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“…For this we shall mainly follow the factorization technique of ref. [1]. We assume a factorization of the Hamiltonian H in the form…”

Section: Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Study of classical mechanical systems with complex potentials

Sinha¹,

Dutta²,

Roy³

2011

Physics Letters A

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Curvature as an Integrable Deformation

Ballesteros

Blasco

Herranz

2019

Integrability, Supersymmetry and Coherent States

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Trends in Supersymmetric Quantum Mechanics

David²

2019

Integrability, Supersymmetry and Coherent States

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Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two Hamiltonians through a finite order differential operator. Some related subjects can be simply analyzed, as the algebras ruling both Hamiltonians and the associated coherent states. The technique has been applied also to periodic potentials, where the spectra consist of allowed and forbidden energy bands. In addition, a link with nonlinear second-order differential equations, and the possibility of generating some solutions, can be explored. Recent applications concern the study of Dirac electrons in graphene placed either in electric or magnetic fields, and the analysis of optical systems whose relevant equations are the same as those of SUSY QM. These issues will be reviewed briefly in this paper, trying to identify the most important subjects explored currently in the literature. KeywordsSupersymmetric quantum mechanics • Coherent states • Painlevé equations • Painlevé transcendents • Polynomial Heisenberg algebras • Factorization method • Exact solutions • Spectral design • Graphene Dedicated to my dear friend and colleague Véronique Hussin. D. J. Fernández C ( )

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Factorizations of one-dimensional classical systems

Cited by 59 publications

References 11 publications

Study of classical mechanical systems with complex potentials

Study of classical mechanical systems with complex potentials

Curvature as an Integrable Deformation

Trends in Supersymmetric Quantum Mechanics

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