Rational extension and Jacobi-type Xm solutions of a quantum nonlinear oscillator

被引：13

作者：

Schulze-Halberg, Axel ^{[1
,2
]}

Roy, Barnana ^{[3
]}

机构：

[1] Indiana Univ Northwest, Dept Math & Actuarial Sci, Gary, IN 46408 USA

[2] Indiana Univ Northwest, Dept Phys, Gary, IN 46408 USA

[3] Indian Stat Inst, Phys & Appl Math Unit, Kolkata 700108, India

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2013年 / 54卷 / 12期

关键词：

ORTHOGONAL POLYNOMIALS; POTENTIALS;

D O I：

10.1063/1.4835575

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X-m exceptional orthogonal polynomials. (C) 2013 AIP Publishing LLC.

引用

页数：12

共 30 条

[1]

Abramowitz M., 1964, HDB MATH FUNCTIONS F

[2]

[Anonymous], 2003, ORTHOGONAL POLYNOMIA

[3]

Bagchi B, 2009, PRAMANA-J PHYS, V73, P337, DOI 10.1007/s12043-009-0126-4

[4] A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour [J].

Carinena, Jose F. ;

Ranada, Manuel F. ;

Santander, Mariano .

ANNALS OF PHYSICS, 2007, 322 (02) :434-459

[5] Exactly Solvable Schrodinger Operators [J].

Derezinski, Jan ;

Wrochna, Michal .

ANNALES HENRI POINCARE, 2011, 12 (02) :397-418

[6] Conditionally exactly solvable potentials and exceptional orthogonal polynomials [J].

Dutta, D. ;

Roy, P. .

JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (04)

[7] On orthogonal polynomials spanning a non-standard flag [J].

Gomez-Ullate, David ;

Kamran, Niky ;

Milson, Robert .

ALGEBRAIC ASPECTS OF DARBOUX TRANSFORMATIONS, QUANTUM INTEGRABLE SYSTEMS AND SUPERSYMMETRIC QUANTUM MECHANICS, 2012, 563 :51-+

[8] An extension of Bochner's problem: Exceptional invariant subspaces [J].

Gomez-Ullate, David ;

Kamran, Niky ;

Milson, Robert .

JOURNAL OF APPROXIMATION THEORY, 2010, 162 (05) :987-1006

[9] An extended class of orthogonal polynomials defined by a Sturm-Liouville problem [J].

Gomez-Ullate, David ;

Kamran, Niky ;

Milson, Robert .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (01) :352-367

[10] Multistep DBT and regular rational extensions of the isotonic oscillator [J].

Grandati, Yves .

ANNALS OF PHYSICS, 2012, 327 (10) :2411-2431

← 1 2 3 →