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Contracted Hamiltonian on Symmetric Space SU(3)/SU(2) and Conserved Quantities

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Abstract

We study the quantum model on symmetric space SU(3)/SU(2). By using the Inonu-Wigner contraction to Lie algebra su(3), we arrive at a special case of three-body Sutherland model. It has shown that by calculating conservative quantities of this model, it has Poincare Lie algebra, too.

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References

  1. Grabowski, J., Landi, G., Marmo, G., Vilasi, G.: Generalized reduction procedure: symplectic and poisson formalism. Fortschr. Phys. 42, 393–427 (1994)

    Article  MathSciNet  Google Scholar 

  2. Morse, P.M.: Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 34, 57 (1929)

    Article  ADS  Google Scholar 

  3. Poschl, G., Teller, E.: Bemerkungen zur Quantenmechanik des Anharmonischen Oszillators. Z. Phys. 83, 143 (1933)

    Article  ADS  Google Scholar 

  4. Winternitz, P., Smorodinsky, Ya.A., Uhlir, M., Frits, I.: Symmetry groups in classical and quantum mechanics. Sov. J. Nucl. Phys. 4, 444 (1967)

    Google Scholar 

  5. Evans, N.W.: Superintegrability in classical mechanics. Phys. Rev. A 41, 5666 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  6. Evans, N.W.: Super-integrability of the Winternitz system. Phys. Lett. A 147, 483 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  7. Evans, N.W.: Group theory of the Smorodinsky-Winternitz system. J. Math. Phys. 32, 3369 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Calogero, F.: Solution of a three-body problem in one dimension. J. Math. Phys. 10, 2191 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  9. Sutherland, B.: Exact results for a quantum many-body problem in one dimension. Phys. Rev. A 4, 2019 (1971)

    Article  ADS  Google Scholar 

  10. Calzada, J.A., Del Olmo, M.A., Rodrguez, M.A.: Pseudo-orthogonal groups and integrable dynamical systems in two dimensions. J. Math. Phys. 40, 188 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Delolmo, M.A., Calzada, J.A., Rodrguez, M.A.: Classical superintegrable SO(p,q) Hamiltonian systems. J. Geom. Phys. 23, 14 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  12. Izmest’ev, A.A., Pogosyan, G.S., Sissakian, A.N., Winternitz, P.: Contractions of Lie algebras and separation of variables. J. Phys. A, Math. Gen. 29, 5949 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. Panahi, H., Jafarizadeh, M.A.: Two and three dimensional Hamiltonians with generalized and ordinary shape invariance symmetry. J. Math. Phys. 46, 012103 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  14. Rowe, D.J., Sanders, B.C., De Guise, H.: Representations of the Weyl group and Wigner functions for SU(3). J. Math. Phys. 40, 3604 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Gilmore, R.: Lie Groups, Lie Algebra and Some of Their Applications. Wiley, New York (2006)

    Google Scholar 

  16. Roman, P.: Introduction to Quantum Field Theory. Wiley, New York (1969)

    MATH  Google Scholar 

  17. Goldstein, H., Poole, C., Safko, J.: Classical Mechanics. Addison Wesley, Reading (2000)

    Google Scholar 

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Panahi, H., Rahmati, H. Contracted Hamiltonian on Symmetric Space SU(3)/SU(2) and Conserved Quantities. Int J Theor Phys 50, 200–207 (2011). https://doi.org/10.1007/s10773-010-0508-x

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  • DOI: https://doi.org/10.1007/s10773-010-0508-x

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