Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM - INSPIRE

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Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM

C. Quesne
(
- Brussels U., PNTPM
)

Oct, 2011

15 pages

Published in:

Int.J.Mod.Phys.A 26 (2011) 5337-5347

e-Print:

1110.3958 [math-ph]

DOI:

10.1142/S0217751X11054942

Report number:

ULB-229-CQ-11-4

View in:

reference search33 citations

Citations per year

Abstract: (arXiv)

A previous study of exactly solvable rationally-extended radial oscillator potentials and corresponding Laguerre exceptional orthogonal polynomials carried out in second-order supersymmetric quantum mechanics is extended to

k

th-order one. The polynomial appearing in the potential denominator and its degree are determined. The first-order differential relations allowing one to obtain the associated exceptional orthogonal polynomials from those arising in a (

k-1

)th-order analysis are established. Some nontrivial identities connecting products of Laguerre polynomials are derived from shape invariance.

Note:

15 pages, no figure; published version

03.65.Fd
03.65.Ge
Quantum mechanics
supersymmetry
orthogonal polynomials

References(37)

Figures(0)

[1]

D. Gómez-Ullate
,
N. Kamran
,
R. Milson

- J.Math.Anal.Appl. 359 352
•
e-Print:
- 0807.3939

[2]

D. Gómez-Ullate
,
N. Kamran
,
R. Milson

- J.Approx.Theor. 162 987
•
e-Print:
- 0805.3376

[3]

C. Quesne

- J.Phys.A 41 392001
•
e-Print:
- 0807.4087

[4]

Derivation of Exact Spectra of the Schrodinger Equation by Means of Supersymmetry

L.E. Gendenshtein
(
- Kharkov, KIPT
)

- JETP Lett. 38 (1983) 356-359,
- Pisma Zh.Eksp.Teor.Fiz. 38 (1983) 299-302,
- Pisma Zh. Eksp. Teor. Fiz. 38 ( 1983) 299-302

[5]

Supersymmetry and quantum mechanics

Fred Cooper
(
- Los Alamos
)
,
Avinash Khare
(
- Bhubaneswar, Inst. Phys.
)
,
Uday Sukhatme
(
- Illinois U., Chicago
)

- Phys.Rept. 251 (1995) 267-385
•
e-Print:
- hep-th/9405029
•
DOI:
- 10.1016/0370-1573(94)00080-M

[6]

Shape invariant potentials depending on n parameters transformed by translation

Jose F. Carinena
(
- Zaragoza U.
)
,
Arturo Ramos
(
- Zaragoza U.
)

- J.Phys.A 33 (2000) 3467-3481
•
e-Print:
- hep-th/0003266
•
DOI:
- 10.1088/0305-4470/33/17/305

[7]

Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry

- Pramana 73 (2009) 337-347
•
e-Print:
- 0812.1488
•
DOI:
- 10.1007/s12043-009-0126-4

[8]

C. Quesne

- SIGMA 5 084
•
e-Print:
- 0906.2331

[9]

The Inverse Darboux transformation and exactly solvable deformations of shape invariant potentials

David Gomez-Ullate
(
- Montreal U., CRM
)
,
Niky Kamran
(
- McGill U.
)
,
Robert Milson
(
- Dalhousie U.
)

- J.Phys.A 37 (2004) 1780-1804
•
e-Print:
- quant-ph/0308062
•
DOI:
- 10.1088/0305-4470/37/5/022

[10]

D. Gómez-Ullate
,
N. Kamran
,
R. Milson

- J.Phys.A 37 10065

[11]

Infinitely many shape invariant potentials and new orthogonal polynomials

Satoru Odake
(
- Shinshu U.
)
,
Ryu Sasaki
(
- Kyoto U., Yukawa Inst., Kyoto
)

- Phys.Lett.B 679 (2009) 414-417
•
e-Print:
- 0906.0142
•
DOI:
- 10.1016/j.physletb.2009.08.004

[12]

Another set of infinitely many exceptional $(X_{\ell})$ Laguerre polynomials

- Phys.Lett.B 684 (2010) 173-176
•
e-Print:
- 0911.3442
•
DOI:
- 10.1016/j.physletb.2009.12.062

[13]

Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials

Satoru Odake
(
- Shinshu U.
)
,
Ryu Sasaki
(
- Kyoto U., Yukawa Inst., Kyoto
)

- J.Math.Phys. 51 (2010) 053513
•
e-Print:
- 0911.1585
•
DOI:
- 10.1063/1.3371248

[14]

Properties of the exceptional ( $X_{\ell}$ ) Laguerre and Jacobi polynomials

- SIGMA 7 (2011) 107
•
e-Print:
- 0912.5447
•
DOI:
- 10.3842/SIGMA.2011.107

[15]

D. Gómez-Ullate
,
N. Kamran
,
R. Milson

- J.Phys.A 43 434016
•
e-Print:
- 1002.2666

[16]

D. Gómez-Ullate
,
N. Kamran
,
R. Milson

e-Print:
- 1101.5584

[17]

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

Ryu Sasaki
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Satoshi Tsujimoto
(
- Kyoto U.
)
,
Alexei Zhedanov
(
- Kyoto U. and
- Donetsk, FTI
)

- J.Phys.A 43 (2010) 315204
•
e-Print:
- 1004.4711
•
DOI:
- 10.1088/1751-8113/43/31/315204

[18]

Solvable rational extensions of the isotonic oscillator

Yves Grandati
(
- Paul Verlaine U., Metz
)

- Annals Phys. 326 (2011) 2074-2090
•
e-Print:
- 1101.0055
•
DOI:
- 10.1016/j.aop.2011.03.001

[19]

C.-L. Ho

- Prog.Theor.Phys. 126 185
•
e-Print:
- 1104.3511

[20]

Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation

- Phys.Rev.Lett. 105 (2010) 210402
•
e-Print:
- 1008.2035
•
DOI:
- 10.1103/PhysRevLett.105.210402

[21]

Method for Generating Additive Shape Invariant Potentials from an Euler Equation

- J.Phys.A 44 (2011) 275307
•
e-Print:
- 1103.1169
•
DOI:
- 10.1088/1751-8113/44/27/275307

[22]

A. Ramos

- J.Phys.A 44 342001
•
e-Print:
- 1106.3732

[23]

D. Gómez-Ullate
,
N. Kamran
,
R. Milson

e-Print:
- 1103.5724

[24]

Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials

Satoru Odake
(
- Shinshu U.
)
,
Ryu Sasaki
(
- Kyoto U., Yukawa Inst., Kyoto
)

- Phys.Lett.B 702 (2011) 164-170
•
e-Print:
- 1105.0508
•
DOI:
- 10.1016/j.physletb.2011.06.075

[25]

Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials

C. Quesne
(
- Brussels U., PNTPM
)

- Mod.Phys.Lett.A 26 (2011) 1843-1852
•
e-Print:
- 1106.1990
•
DOI:
- 10.1142/S0217732311036383

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