An algebraic approach to a harmonic oscillator plus an inverse square potential in two dimensions

Shi Hai Dong; Guo Hua Sun; M. Lozada-Cassou

doi:10.1142/S0217751X05022305

An algebraic approach to a harmonic oscillator plus an inverse square potential in two dimensions

Shi Hai Dong, Guo Hua Sun, M. Lozada-Cassou

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

11 Scopus citations

Abstract

The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU(1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and ρd/dρ with ρ = r². We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r → ir.

Original language	English
Pages (from-to)	5663-5670
Number of pages	8
Journal	International Journal of Modern Physics A
Volume	20
Issue number	24
DOIs	https://doi.org/10.1142/S0217751X05022305
State	Published - 30 Sep 2005
Externally published	Yes

Keywords

Inverse square potential
Ladder operators
Matrix elements
SU(1, 1) group

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10.1142/S0217751X05022305

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title = "An algebraic approach to a harmonic oscillator plus an inverse square potential in two dimensions",

abstract = "The exact solutions of the Schr{\"o}dinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU(1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and ρd/dρ with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r → ir.",

keywords = "Inverse square potential, Ladder operators, Matrix elements, SU(1, 1) group",

author = "Dong, {Shi Hai} and Sun, {Guo Hua} and M. Lozada-Cassou",

note = "Funding Information: This work is supported by CONACyT, Mexico, under projects L007E and C086A. We would like to thank the referee for the positive and invaluable suggestions, from which the manuscript is improved greatly.",

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T1 - An algebraic approach to a harmonic oscillator plus an inverse square potential in two dimensions

AU - Dong, Shi Hai

AU - Sun, Guo Hua

AU - Lozada-Cassou, M.

N1 - Funding Information: This work is supported by CONACyT, Mexico, under projects L007E and C086A. We would like to thank the referee for the positive and invaluable suggestions, from which the manuscript is improved greatly.

PY - 2005/9/30

Y1 - 2005/9/30

N2 - The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU(1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and ρd/dρ with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r → ir.

AB - The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU(1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and ρd/dρ with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r → ir.

KW - Inverse square potential

KW - Ladder operators

KW - Matrix elements

KW - SU(1, 1) group

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U2 - 10.1142/S0217751X05022305

DO - 10.1142/S0217751X05022305

M3 - Artículo

SN - 0217-751X

VL - 20

SP - 5663

EP - 5670

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 24

ER -

An algebraic approach to a harmonic oscillator plus an inverse square potential in two dimensions

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Keywords

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