Generation of a Novel Exactly Solvable Potential

Jonathan Bougie; Asim Gangopadhyaya; Jeffry V. Mallow,; Constantin Rasinariu

doi:10.1016/j.physleta.2015.06.058

Generation of a Novel Exactly Solvable Potential

Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow,, Constantin Rasinariu

Department of Physics

Research output: Contribution to journal › Article › peer-review

Abstract

We report a new shape-invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of “conventional” SI superpotentials that do not depend explicitly on Planck's constant &hstrok; is complete. Additionally, a set of “extended” superpotentials has been identified, each containing a conventional superpotential as a kernel and additional &hstrok; -dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.

Original language	American English
Journal	Physics: Faculty Publications and Other Works
Volume	379
Issue number	37
DOIs	https://doi.org/10.1016/j.physleta.2015.06.058
State	Published - Oct 2 2015

Keywords

Supersymmetric quantum mechanics
Shape invariance
Exactly solvable systems
Extended potentials
Isospectral deformation

Disciplines

Physics
Quantum Physics

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title = "Generation of a Novel Exactly Solvable Potential",

abstract = " We report a new shape-invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of “conventional” SI superpotentials that do not depend explicitly on Planck's constant &hstrok; is complete. Additionally, a set of “extended” superpotentials has been identified, each containing a conventional superpotential as a kernel and additional &hstrok; -dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.",

keywords = "Supersymmetric quantum mechanics, Shape invariance, Exactly solvable systems, Extended potentials, Isospectral deformation",

author = "Jonathan Bougie and Asim Gangopadhyaya and Mallow,, {Jeffry V.} and Constantin Rasinariu",

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AU - Gangopadhyaya, Asim

AU - Mallow,, Jeffry V.

AU - Rasinariu, Constantin

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Y1 - 2015/10/2

N2 - We report a new shape-invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of “conventional” SI superpotentials that do not depend explicitly on Planck's constant &hstrok; is complete. Additionally, a set of “extended” superpotentials has been identified, each containing a conventional superpotential as a kernel and additional &hstrok; -dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.

AB - We report a new shape-invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of “conventional” SI superpotentials that do not depend explicitly on Planck's constant &hstrok; is complete. Additionally, a set of “extended” superpotentials has been identified, each containing a conventional superpotential as a kernel and additional &hstrok; -dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.

KW - Supersymmetric quantum mechanics

KW - Shape invariance

KW - Exactly solvable systems

KW - Extended potentials

KW - Isospectral deformation

UR - https://ecommons.luc.edu/physics_facpubs/63

UR - http://arxiv.org/pdf/1506.08809.pdf

U2 - 10.1016/j.physleta.2015.06.058

DO - 10.1016/j.physleta.2015.06.058

M3 - Article

VL - 379

JO - Physics: Faculty Publications and Other Works

JF - Physics: Faculty Publications and Other Works

IS - 37

ER -

Generation of a Novel Exactly Solvable Potential

Abstract

Keywords

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