Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach

The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension o...

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Published inAnnals of physics Vol. 324; no. 5; pp. 1095 - 1104
Main Author Ho, Choon-Lin
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.05.2009
Elsevier BV
Subjects
Bethe ansatz equations
COORDINATES
EIGENFUNCTIONS
EIGENVALUES
EQUATIONS
EXACT SOLUTIONS
Exact solvability
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical models
MORSE POTENTIAL
Prepotential
Quantum physics
Quasi-exact solvability
02.30.Ik
Prepotential
03.65.Ca
03.65.Ge
Bethe ansatz equations
Exact solvability
Quasi-exact solvability
Online AccessGet full text

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Abstract The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way.
AbstractList The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way.
The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way. [PUBLICATION ABSTRACT]
Author Ho, Choon-Lin
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10.1016/j.aop.2008.04.010
10.1088/0305-4470/37/1/015
10.1007/BF01466727
10.1063/1.2349485
10.1007/BF02099042
10.1016/0375-9601(87)90456-7
10.1088/0305-4470/35/33/306
10.1088/0305-4470/35/39/312
10.1016/j.aop.2004.01.007
10.1143/PTP.103.463
10.1016/0370-1573(94)00080-M
10.1016/j.aop.2005.12.005
10.1063/1.2162334
10.1088/0305-4470/33/49/303
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Keywords 02.30.Ik
Prepotential
03.65.Ca
03.65.Ge
Bethe ansatz equations
Exact solvability
Quasi-exact solvability
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References González, Kamran, Olver (bib4) 1993; 153
Odake, Sasaki (bib11) 2006; 47
Cooper, Khare, Sukhatme (bib1) 1995; 251
C.-L. Ho, Prepotential approach to exact and quasi-exact solvabilities of Hermitian and non-Hermitian Hamiltonians (Talk presented at “Conference in Honor of CN Yang’s 85th Birthday”, 31 October–3 November, 2007, Singapore)
[hep-th].
Turbiner (bib3) 1988; 118
Turbiner, Ushveridze (bib2) 1987; 126
Ho, Roy, Ho, Roy, Ho (bib10) 2003; 36
Szegö (bib12) 1939; vol. 23
Ushveridze, Ushveridze (bib5) 1988; 2
Kamran, Milson, Olver (bib7) 1999
Post, Turbiner (bib6) 1995; 3
Corrigan, Sasaki, Bordner, Manton, Sasaki, Khastgir, Pocklington, Sasaki, Odake, Sasaki, Loris, Sasaki, Sasaki, Takasaki (bib9) 2002; 35
Ushveridze (10.1016/j.aop.2008.10.004_bib5_2) 1994
Bordner (10.1016/j.aop.2008.10.004_bib9_2) 2000; 103
Turbiner (10.1016/j.aop.2008.10.004_bib2) 1987; 126
Odake (10.1016/j.aop.2008.10.004_bib9_4) 2002; 35
González (10.1016/j.aop.2008.10.004_bib4) 1993; 153
Odake (10.1016/j.aop.2008.10.004_bib11) 2006; 47
Turbiner (10.1016/j.aop.2008.10.004_bib3) 1988; 118
Ho (10.1016/j.aop.2008.10.004_bib10_1) 2003; 36
Kamran (10.1016/j.aop.2008.10.004_bib7) 1999
Khastgir (10.1016/j.aop.2008.10.004_bib9_3) 2000; 33
Post (10.1016/j.aop.2008.10.004_bib6) 1995; 3
Sasaki (10.1016/j.aop.2008.10.004_bib9_6) 2006; 47
Ho (10.1016/j.aop.2008.10.004_bib10_2) 2004; 312
Loris (10.1016/j.aop.2008.10.004_bib9_5) 2004; 37
Ho (10.1016/j.aop.2008.10.004_bib10_3) 2006; 321
Ho (10.1016/j.aop.2008.10.004_bib8_1) 2008; 323
Ushveridze (10.1016/j.aop.2008.10.004_bib5_1) 1988; 2
10.1016/j.aop.2008.10.004_bib8_2
Szegö (10.1016/j.aop.2008.10.004_bib12) 1939; vol. 23
Cooper (10.1016/j.aop.2008.10.004_bib1) 1995; 251
Corrigan (10.1016/j.aop.2008.10.004_bib9_1) 2002; 35
References_xml – volume: 2
  start-page: 50, 54
  year: 1988
  ident: bib5
  article-title: Quasi-Exactly Solvable Models in Quantum Mechanics
  publication-title: Sov. Phys.-Lebedev Inst. Rep.
  contributor:
    fullname: Ushveridze
– volume: 118
  start-page: 467
  year: 1988
  ident: bib3
  publication-title: Commun. Math. Phys.
  contributor:
    fullname: Turbiner
– volume: 36
  start-page: 4617
  year: 2003
  ident: bib10
  publication-title: J. Phys. A
  contributor:
    fullname: Ho
– volume: 47
  start-page: 102102
  year: 2006
  ident: bib11
  publication-title: J. Math. Phys.
  contributor:
    fullname: Sasaki
– year: 1999
  ident: bib7
  publication-title: Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems
  contributor:
    fullname: Olver
– volume: 153
  start-page: 117
  year: 1993
  ident: bib4
  publication-title: Commun. Math. Phys.
  contributor:
    fullname: Olver
– volume: 35
  start-page: 7017
  year: 2002
  ident: bib9
  publication-title: J. Phys. A
  contributor:
    fullname: Takasaki
– volume: 126
  start-page: 181
  year: 1987
  ident: bib2
  publication-title: Phys. Lett. A
  contributor:
    fullname: Ushveridze
– volume: 3
  start-page: 113
  year: 1995
  ident: bib6
  publication-title: Russ. J. Math. Phys.
  contributor:
    fullname: Turbiner
– volume: 251
  start-page: 267
  year: 1995
  ident: bib1
  publication-title: Phys. Rep.
  contributor:
    fullname: Sukhatme
– volume: vol. 23
  year: 1939
  ident: bib12
  article-title: Orthogonal Polynomials
  publication-title: American Mathematical Society’s Colloquium Publications
  contributor:
    fullname: Szegö
– volume: 36
  start-page: 4617
  year: 2003
  ident: 10.1016/j.aop.2008.10.004_bib10_1
  publication-title: J. Phys. A
  doi: 10.1088/0305-4470/36/16/311
  contributor:
    fullname: Ho
– volume: 323
  start-page: 2241
  year: 2008
  ident: 10.1016/j.aop.2008.10.004_bib8_1
  publication-title: Ann. Phys.
  doi: 10.1016/j.aop.2008.04.010
  contributor:
    fullname: Ho
– volume: 37
  start-page: 211
  year: 2004
  ident: 10.1016/j.aop.2008.10.004_bib9_5
  publication-title: J. Phys. A
  doi: 10.1088/0305-4470/37/1/015
  contributor:
    fullname: Loris
– volume: 118
  start-page: 467
  year: 1988
  ident: 10.1016/j.aop.2008.10.004_bib3
  publication-title: Commun. Math. Phys.
  doi: 10.1007/BF01466727
  contributor:
    fullname: Turbiner
– volume: 2
  start-page: 50, 54
  year: 1988
  ident: 10.1016/j.aop.2008.10.004_bib5_1
  publication-title: Sov. Phys.-Lebedev Inst. Rep.
  contributor:
    fullname: Ushveridze
– volume: 47
  start-page: 102102
  year: 2006
  ident: 10.1016/j.aop.2008.10.004_bib11
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2349485
  contributor:
    fullname: Odake
– volume: 153
  start-page: 117
  year: 1993
  ident: 10.1016/j.aop.2008.10.004_bib4
  publication-title: Commun. Math. Phys.
  doi: 10.1007/BF02099042
  contributor:
    fullname: González
– volume: 126
  start-page: 181
  year: 1987
  ident: 10.1016/j.aop.2008.10.004_bib2
  publication-title: Phys. Lett. A
  doi: 10.1016/0375-9601(87)90456-7
  contributor:
    fullname: Turbiner
– volume: 35
  start-page: 7017
  year: 2002
  ident: 10.1016/j.aop.2008.10.004_bib9_1
  publication-title: J. Phys. A
  doi: 10.1088/0305-4470/35/33/306
  contributor:
    fullname: Corrigan
– volume: vol. 23
  year: 1939
  ident: 10.1016/j.aop.2008.10.004_bib12
  article-title: Orthogonal Polynomials
  contributor:
    fullname: Szegö
– volume: 35
  start-page: 8283
  year: 2002
  ident: 10.1016/j.aop.2008.10.004_bib9_4
  publication-title: J. Phys. A
  doi: 10.1088/0305-4470/35/39/312
  contributor:
    fullname: Odake
– volume: 312
  start-page: 161
  year: 2004
  ident: 10.1016/j.aop.2008.10.004_bib10_2
  publication-title: Ann. Phys.
  doi: 10.1016/j.aop.2004.01.007
  contributor:
    fullname: Ho
– volume: 3
  start-page: 113
  year: 1995
  ident: 10.1016/j.aop.2008.10.004_bib6
  publication-title: Russ. J. Math. Phys.
  contributor:
    fullname: Post
– volume: 103
  start-page: 463
  year: 2000
  ident: 10.1016/j.aop.2008.10.004_bib9_2
  publication-title: Prog. Theor. Phys.
  doi: 10.1143/PTP.103.463
  contributor:
    fullname: Bordner
– volume: 251
  start-page: 267
  year: 1995
  ident: 10.1016/j.aop.2008.10.004_bib1
  publication-title: Phys. Rep.
  doi: 10.1016/0370-1573(94)00080-M
  contributor:
    fullname: Cooper
– volume: 321
  start-page: 2170
  year: 2006
  ident: 10.1016/j.aop.2008.10.004_bib10_3
  publication-title: Ann. Phys.
  doi: 10.1016/j.aop.2005.12.005
  contributor:
    fullname: Ho
– volume: 47
  start-page: 012701
  year: 2006
  ident: 10.1016/j.aop.2008.10.004_bib9_6
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2162334
  contributor:
    fullname: Sasaki
– year: 1994
  ident: 10.1016/j.aop.2008.10.004_bib5_2
  contributor:
    fullname: Ushveridze
– year: 1999
  ident: 10.1016/j.aop.2008.10.004_bib7
  publication-title: Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems
  contributor:
    fullname: Kamran
– ident: 10.1016/j.aop.2008.10.004_bib8_2
– volume: 33
  start-page: 9033
  year: 2000
  ident: 10.1016/j.aop.2008.10.004_bib9_3
  publication-title: J. Phys. A
  doi: 10.1088/0305-4470/33/49/303
  contributor:
    fullname: Khastgir
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Snippet The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being...
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SubjectTerms Bethe ansatz equations
COORDINATES
EIGENFUNCTIONS
EIGENVALUES
EQUATIONS
EXACT SOLUTIONS
Exact solvability
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical models
MORSE POTENTIAL
Prepotential
Quantum physics
Quasi-exact solvability
Title Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach
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