Supersymmetric WKB approach to scattering problems

Dutt, Ranabir; R, De; Adhikari, R.; Comtet, Alain

doi:10.1016/0375-9601(91)90829-w

Cited by 10 publications

(9 citation statements)

References 25 publications

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“…(xiii) SWKB and Tunneling [263,82] Expression for transmission coecient T through potential barriers has been obtained within the SWKB approximation and it has been shown that the analytic continuation of T for the inverted SIP (with translation) leads to the exact bound state spectrum.…”

Section: Orthosupersymmetric Quantum Mechanicsmentioning

confidence: 99%

“…Three of the notable ones are the 1=N expansion within SUSY QM [77], 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]. Further, it is not only exact for large n (as any WKB approximation is) but by construction it is also exact for the ground state of V 1 (x).…”

Section: Introductionmentioning

confidence: 99%

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Supersymmetry and quantum mechanics

1995

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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 m uch deeper understanding of why certain potentials are analytically solvable and an array o f p o w erful 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 eld and other potentials in terms of supersymmetric quantum mechanics. Finally, w e 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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Section: Orthosupersymmetric Quantum Mechanicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Supersymmetry and quantum mechanics

1995

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“…In particular, they diverge at the classical turning points. Also, the transmisson and re8ection coefBcients T and R are not fully given by the semiclassical methods [28].…”

Section: Application To Broken Susy Shape-invariant Potentialsmentioning

confidence: 99%

Semiclassical approach to quantum-mechanical problems with broken supersymmetry

et al. 1993

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“…(xiii) SWKB and Tunneling [263,82] Expression for transmission coefficient T through potential barriers has been obtained within the SWKB approximation and it has been shown that the analytic continuation of T for the inverted SIP (with translation) leads to the exact bound state spectrum.…”

Section: Omitted Topicsmentioning

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]. Further, it is not only exact for large n (as any WKB approximation is) but by construction it is also exact for the ground state of V 1 (x).…”

Section: Introductionmentioning

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.

show abstract

Supersymmetric WKB approach to scattering problems

Cited by 10 publications

References 25 publications

Supersymmetry and quantum mechanics

Supersymmetry and quantum mechanics

Semiclassical approach to quantum-mechanical problems with broken supersymmetry

Parasupersymmetry in quantum mechanics

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