ESTONIAN ACADEMY
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akadeemia kirjastus
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Quantum counterparts of VIIα, IIIα=1, VIα≠1 over the harmonic oscillator in semiclassical approximation; pp. 347–354

Full article in PDF format | doi: 10.3176/proc.2010.4.14

Authors
Eugen Paal, Jüri Virkepu

Abstract
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of some real 3-dimensional Lie algebras. The Jacobi operators of these quantum algebras are studied in semiclassical approximation.
References

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  6. Paal, E. and Virkepu, J. 2D binary operadic Lax representation for harmonic oscillator. In Noncommutative Structures in Mathematics and Physics (Caenepeel, S., Fuchs, J., Gutt, S., Schweigert, C., Stolin, A., and Van Oystaeyen, F., eds). K. Vlaam. Acad. Belgie Wet. Kunsten (KVAB), Brussels, 2010, 209–216.

  7. Paal, E. and Virkepu, J. Operadic representations of harmonic oscillator in some 3d Lie algebras. J. Gen. Lie Theory Appl., 2009, 3, 53–59.
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  8. Paal, E. and Virkepu, J. Dynamical deformations of 3d Lie algebras in Bianchi classification over harmonic oscillator. J. Math. Phys., 2009, 50, 053523.
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  9. Paal, E. and Virkepu, J. Quantum counterparts of three-dimensional real Lie algebras over harmonic oscillator. Centr. Eur. J. Phys., 2010, 8, 289–295.
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