Discrete repulsive oscillator wavefunctions

For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, and, provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with th...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-12, Vol.42 (48), p.485210-485210 (12)
Main Authors: Muñoz, Carlos A, Rueda-Paz, Juvenal, Wolf, Kurt Bernardo
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, and, provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for. Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/48/485210