Exactness of semiclassical bound state energies for supersymmetric quantum mechanics

Comtet, Alain; Bandrauk, A. D.; Campbell, David

doi:10.1016/0370-2693(85)90160-1

Cited by 239 publications

(180 citation statements)

References 11 publications

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“…In particular it has provided exact solutions of the Schrödinger equation for a class of so called shape invariant potential [4]. It has also inspired a new method of semi-classical quantization [5,6]. In the context of disordered systems, i.e.…”

Section: -Introductionmentioning

confidence: 99%

Localization Properties in One-Dimensional Disordered Supersymmetric Quantum Mechanics

Comtet¹,

Desbois²,

Monthus³

1995

Annals of Physics

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-A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential φ(x) is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which φ(x) is kept constant are distributed according to a broad distribution. Various applications of this model are considered. IPNO/TH 94 -33APRIL 94

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Section: -Introductionmentioning

confidence: 99%

Localization Properties in One-Dimensional Disordered Supersymmetric Quantum Mechanics

Comtet¹,

Desbois²,

Monthus³

1995

Annals of Physics

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“…For this case, the O(h) term in (271) exactly giveshπ/2, so that to leading order inh the SWKB quantization condition when SUSY is unbroken is [79,80] …”

Section: Swkb Quantization Condition For Unbroken Supersymmetrymentioning

confidence: 99%

“…It has a wider range of applicability than standard perturbation theory which is restricted to perturbing potentials with small coupling constants. The purpose of this section is to describe and give applications of the supersymmetric WKB method (henceforth called SWKB) [79,80] which has been inspired by supersymmetric quantum mechanics.…”

Section: Supersymmetric Wkb Approximationmentioning

confidence: 99%

“…Three of the notable ones are the 1/N expansion within SUSY QM [77], δ expansion for the superpotential [78] and a SUSY inspired WKB approximation (SWKB) in quantum mechanics for the case of unbroken SUSY [79,80,81]. It turns out that the SWKB approximation preserves the exact SUSY rela-tions between the energy eigenvalues as well as the scattering amplitudes of the partner potentials [82].…”

Section: Introductionmentioning

confidence: 99%

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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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“…The algebraic techniques are related to the inspection of the Hamiltonian of quantum system as in the supersymmetric quantum mechanics (SUSYQM) [13,14,15] and closely to the factorization method [16,17]. Other methods are based on the proper and exact quantization rule [18,19,20,21] and the SWKB method [22]. Except for the previous methods, quasilinearization method (QLM) is dealing with physical potentials numerically [23,24].…”

mentioning

confidence: 99%

Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

Ikhdair

Falaye

2013

Chemical Physics

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We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrödinger equation in the presence of Pöschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrödinger system. Rotational-Vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as S-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U , specific heat C, free energy F and entropy S.

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Exactness of semiclassical bound state energies for supersymmetric quantum mechanics

Cited by 239 publications

References 11 publications

Localization Properties in One-Dimensional Disordered Supersymmetric Quantum Mechanics

Localization Properties in One-Dimensional Disordered Supersymmetric Quantum Mechanics

Parasupersymmetry in quantum mechanics

Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

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