Supersymmetric approach for generating quasi-exactly solvable potentials with arbitrary two known eigenstates

Tkachuk, V. M.

doi:10.1088/0305-4470/34/32/313

Cited by 5 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…On starting from some assumption for the latter, it is possible to construct QES potentials with two known eigenstates (the ground and first excited states again). This method has also been generalized for generating QES potentials with arbitrary two known eigenstates [32], as well as QES potentials with three known eigenstates [33].…”

Section: Introductionmentioning

confidence: 99%

Deformed shape invariance symmetry and potentials in curved space with two known eigenstates

Quesne

2018

Journal of Mathematical Physics

View full text Add to dashboard Cite

We consider two families of extensions of the oscillator in a d-dimensional constantcurvature space and analyze them in a deformed supersymmetric framework, wherein the starting oscillator is known to exhibit a deformed shape invariance property. We show that the first two members of each extension family are also endowed with such a property provided some constraint conditions relating the potential parameters are satisfied, in other words they are conditionally deformed shape invariant. Since, in the second step of the construction of a partner potential hierarchy, the constraint conditions change, we impose compatibility conditions between the two sets to build potentials with known ground and first excited states. To extend such results to any members of the two families, we devise a general method wherein the first two superpotentials, the first two partner potentials, and the first two eigenstates of the starting potential are built from some generating function W + (r) (and its accompanying function W − (r)).

show abstract

Section: Introductionmentioning

confidence: 99%

Deformed shape invariance symmetry and potentials in curved space with two known eigenstates

Quesne

2018

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…In this paper we develop a simple method for generation of QES potentials with two known eigenstates in arbitrary dimension. For one-dimensional case the problem of constructing QES potential with two known levels was solved completely in the frame of SUSY quantum mechanics [33,34,35] or using a simple method in which two wave functions are chosen in such a way that they lead to the same potential [36,37]. Just this method will be generalized for multidimensional case.…”

Section: Introductionmentioning

confidence: 99%

“…Note that in fact the idea of the papers [33,34,35,36,37] is based on the inverse method. For the first time this method was used by Ushveridze [14] for construction QES potentials.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional quasi-exactly solvable potentials with two known eigenstates

Tkachuk

Fityo

2003

Physics Letters A

View full text Add to dashboard Cite

“…A distinctive feature of this method is that in contrast with other ones, it does not require the knowledge of an initial QES potential for constructing a new one. Later on, the procedure was extended to deal with QES potentials with two arbitrary eigenstates [14] or with three eigenstates [15].…”

Section: Introductionmentioning

confidence: 99%

Pt-Symmetric Nonpolynomial Oscillators and Hyperbolic Potential With Two Known Real Eigenvalues in a Susy Framework

Bagchi

Quesne

2002

Mod. Phys. Lett. A

View full text Add to dashboard Cite

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasiexactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified non-polynomial oscillators and of a complexified hyperbolic potential, to demonstrate how our scheme works in practice. For the former we provide a connection with the sl(2) method, illustrating the comparative advantages of the supersymmetric one.Running head: SUSY and PT-symmetric potentials PACS: 03.65.Fd, 03.65.Ge

show abstract

Supersymmetric approach for generating quasi-exactly solvable potentials with arbitrary two known eigenstates

Cited by 5 publications

References 25 publications

Deformed shape invariance symmetry and potentials in curved space with two known eigenstates

Deformed shape invariance symmetry and potentials in curved space with two known eigenstates

Multidimensional quasi-exactly solvable potentials with two known eigenstates

Pt-Symmetric Nonpolynomial Oscillators and Hyperbolic Potential With Two Known Real Eigenvalues in a Susy Framework

Contact Info

Product

Resources

About