Deformed su (1,1) Algebra as a Model for Quantum Oscillators

被引:8
作者
Jafarov, Elchin I. [1 ,2 ]
Stoilova, Neli I. [3 ]
Van der Jeugt, Joris [1 ]
机构
[1] Univ Ghent, Dept Appl Math & Comp Sci, B-9000 Ghent, Belgium
[2] Azerbaijan Natl Acad Sci, Inst Phys, AZ-1143 Baku, Azerbaijan
[3] Bulgarian Acad Sci, Inst Nucl Res & Nucl Energy, BU-1784 Sofia, Bulgaria
关键词
oscillator model; deformed algebra su(1,1); Meixner-Pollaczek polynomial; continuous dual Hahn polynomial; FINITE 2-DIMENSIONAL OSCILLATOR; POLYNOMIALS; ANALOGS; LIE;
D O I
10.3842/SIGMA.2012.025
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The Lie algebra su(1, 1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1, 1) can be extended to representations of this deformed algebra su (1, 1)(gamma). Just as the positive discrete series representations of su(1, 1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su (1, 1)(gamma) can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models.
引用
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页数:15
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