New Solvable Singular Potentials

R. Dutt; Asim Gangopadhyaya; C. Rasinariu; Uday P. Sukhatne

doi:10.1088/0305-4470/34/19/311

New Solvable Singular Potentials

R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday P. Sukhatne

Department of Physics

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

Abstract

We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.

Original language	American English
Journal	Physics: Faculty Publications and Other Works
Volume	34
Issue number	4129
DOIs	https://doi.org/10.1088/0305-4470/34/19/311
State	Published - Mar 1 2001

Keywords

solvable potentials

Disciplines

Physics

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Cite this

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title = "New Solvable Singular Potentials",

abstract = " We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P{\"o}schl-Teller I and P{\"o}schl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.",

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N2 - We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.

AB - We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.

KW - solvable potentials

UR - https://ecommons.luc.edu/physics_facpubs/11

U2 - 10.1088/0305-4470/34/19/311

DO - 10.1088/0305-4470/34/19/311

M3 - Article

VL - 34

JO - Physics: Faculty Publications and Other Works

JF - Physics: Faculty Publications and Other Works

IS - 4129

ER -

New Solvable Singular Potentials

Abstract

Keywords

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