Higher Order Parasupersymmetric Quantum Mechanics

Durand, Stéphane; Mayrand, Michel; Spiridonov, V. P.; Vinet, Luc

doi:10.1142/s0217732391003651

Cited by 24 publications

(22 citation statements)

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“…Notorious supersymmetric Hamiltonians are obtained by unification of any two successive pairs H n ,H n + \ in a diagonal 2x2 matrix [4]. Analogous construction for the whole chain (3) was called an order N parasupersymmetric quantum mechanics [5,6]. In the latter case, relations (1) naturally arise as the diagonality conditions of the general (7V+ 1 )x (/V + 1 )-dimensional parasupersymmetric Hamiltonian.…”

Section: Exactly Solvable Potentials and Quantum Algebrasmentioning

confidence: 99%

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Exactly solvable potentials and quantum algebras

1992

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A set of exactly solvable one-dimensional quantum-mechanical potentials is described. It is defined by a finite-difference-difTerential equation generating in the limiting cases the Rosen-Morse, harmonic, and Poschl-Teller potentials. A general solution includes Shabafs infinite number soliton system and leads to raising and lowering operators satisfying a ^-deformed harmonic-oscillator algebra. In the latter case the energy spectrum is purely exponential and physical states form a reducible representation of the quantum conformal algebra su

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Section: Exactly Solvable Potentials and Quantum Algebrasmentioning

confidence: 99%

“…Any exactly solvable discrete spectrum problem can be represented in the forms (2)- (6). Sometimes it is easier to solve the Schrodinger equation by direct construction of the chain of associated Hamiltonians (3)-this is the essence of the so-called factorization method [7][8][9].…”

Section: Exactly Solvable Potentials and Quantum Algebrasmentioning

confidence: 99%

Exactly solvable potentials and quantum algebras

1992

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“…Initially it was felt that the generalization to order p was not possible in the sense that the PSQM of order p cannot be characterized with one universal algebraic relation [243]. However, later on, one was indeed able to construct such a PSQM of order p [107].…”

Section: Parasupersymmetric Quantum Mechanics and Beyondmentioning

confidence: 99%

Parasupersymmetry in quantum mechanics

Khare

1993

Journal of Mathematical Physics

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In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all 1 have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p.

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“…A fundamental difference between quantum and classical physics is the possible existence of quantum entanglement between distinct systems (Einstein et al, 1935;SchrÖdinger, 1935). It exhibits the nature of nonlocal correlation between quantum systems, and plays an essential role in various fields of quantum information theory and provides potential resources for communication and information processing (Bennett et al, 1993(Bennett et al, , 1996Bennett and Wiesner, 1992).…”

Section: Introductionmentioning

confidence: 99%