Application of nonlinear deformation algebra to a physical system with Pöschl-Teller potential

Quesne, Christiane

doi:10.1088/0305-4470/31/30/012

Cited by 26 publications

(38 citation statements)

References 27 publications

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“…A general method for developing nonlinear deformations of the su(2) and su(1,1) algebras has been developed in 135,136,137 . Using this method nonlinear deformations of the su(1,1) algebra related to the Pöschl-Teller potential have been obtained in 138,139 .…”

Section: Generalized Deformed Su(2) and Su(11) Algebrasmentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)⊃so (3) model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator and its relation to the nuclear shell model, the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to the structure of molecules and of atomic clusters, as well as an outlook are also given.

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Section: Generalized Deformed Su(2) and Su(11) Algebrasmentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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“…22. The proof, which the generators given by (10) satisfy the so(3) algebraic commutation relations, is very tedious but feasible.…”

Section: So(3) Algebra Associated With the Morse Potentialmentioning

confidence: 99%

so(3) algebraic approach to the Morse potential

Zhang

Yang

Guo

2013

Journal of Mathematical Physics

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We construct so(3) algebra associated with the Morse potential and show that these operators obey so(3) commutation relations. A so(3) algebraic method is proposed in order to obtain the eigenvalues and eigenfunctions of the Morse potential. This method exhibits that Cartan operatorĴ z , the lowering operatorĴ − , and the raising operatorĴ + determine successfully energy eigenvalues, the lowest energy eigenfunction, and excited energy eigenfunctions, respectively. C 2013 AIP Publishing LLC.

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“…In Secs. III and IV, we construct two appropriate new polynomial su (1,1) algebras for the first and second PT potential by imitating Chen et al's 24 …”

Section: Introductionmentioning

confidence: 99%

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

Zhang

2013

Journal of Mathematical Physics

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Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operatorsK ± of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derived naturally from the polynomial su(1, 1) algebras built by us. C 2013 AIP Publishing LLC.

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Application of nonlinear deformation algebra to a physical system with Pöschl-Teller potential

Cited by 26 publications

References 27 publications

Quantum groups and their applications in nuclear physics

Quantum groups and their applications in nuclear physics

so(3) algebraic approach to the Morse potential

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

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