A quasi-exactly solvable problem without Si(2) symmetry

Jatkar, Dileep P.; Kumar, C. N.; Khare, Avinash

doi:10.1016/0375-9601(89)90313-7

Cited by 32 publications

(37 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The basic idea consists in finding such a pair of W (x) and W 1 (x) that satisfies equation (10). To do this we rewrite equation (10) in the following form…”

Section: Qes Potentials With Two Known Eigenstatesmentioning

confidence: 99%

Supersymmetric method for constructing quasi-exactly and conditionally-exactly solvable potentials

Tkachuk¹

1999

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

“…The basic idea consists in finding such a pair of W (x) and W 1 (x) that satisfies equation (10). To do this we rewrite equation (10) in the following form…”

Section: Qes Potentials With Two Known Eigenstatesmentioning

confidence: 99%

Supersymmetric method for constructing quasi-exactly and conditionally-exactly solvable potentials

Tkachuk¹

1999

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

“…This example suggests that the stability analysis about other classical solutions (solitons, kinks....) might also be related to QES systems (see, however, Ref. [12]). …”

Section: Discussionmentioning

confidence: 99%

Quasiexactly solvable 2×2 matrix equations

Brihaye

Kosiński

1994

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Quasi-solvable potentials have been discussed by Shifman and Turbiner [255,256] and using the techniques of SUSY QM a large number of new quasi-solvable problems have been discovered [257].…”

Section: Omitted Topicsmentioning

confidence: 99%

Parasupersymmetry in quantum mechanics

Khare

1993

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

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

A quasi-exactly solvable problem without Si(2) symmetry

Cited by 32 publications

References 18 publications

Supersymmetric method for constructing quasi-exactly and conditionally-exactly solvable potentials

Supersymmetric method for constructing quasi-exactly and conditionally-exactly solvable potentials

Quasiexactly solvable 2×2 matrix equations

Parasupersymmetry in quantum mechanics

Contact Info

Product

Resources

About