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Quantum mechanics in curved space-time

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Abstract.

In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild like metric. As a test, the hydrogen atom spectrum is calculated. A comparison of the calculated spectrum with the numerical data of the deuterium energy levels shows a significant improvement of the accord, and the deviations are almost five times smaller then the ones obtained with the Dirac theory. The implications of the theory considering the strong interactions are also discussed.

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References

  1. P.A.M. Dirac, Proc. Roy. Soc. Lon. A 117, 610 (1930); P.A.M. Dirac, ibid A 126, 360 (1930)

    Google Scholar 

  2. L. Rosenfeld, Ann. Phys. 5, 113 (1930); Z. Phys. 65, 589 (1930)

    Google Scholar 

  3. B.S. DeWitt, Phys. Rev. 160, 1113 (1967)

    CAS  Google Scholar 

  4. J.B. Hartle, S.W. Hawking, Phys. Rev. D 28, 2960 (1983)

    Article  Google Scholar 

  5. L. Parker, Phys. Rev. D 15, 1922 (1980)

    Article  Google Scholar 

  6. L. Landau, E. Lifshitz, The Classical Theory of Fields. Pergamon, Oxford, 1975

  7. S. Weinberg, Gravitation and cosmology: principles and applications of the general theory of relativity. Wiley, New York, 1972

  8. R.A. Mould, Basic Relativity. Springer-Verlag, New York, 1994

  9. M.E. Rose, Relativistic electron theory. Wiley New York, 1961

  10. W. Pauli, General Principles of Quantum Mechanics. Springer-Verlag, New York, 1980

  11. L.I. Schiff, Quantum mechanics. McGraw-Hill, Singapore, 1968

  12. J.D. Bjorken, S. Drell, Relativistic quantum mechanics. McGraw-Hill, New York, 1964

  13. A. Sommerfeld, Ann. Phys. 51, 1 (1916)

    CAS  Google Scholar 

  14. R. Penrose, Phys. Rev. Lett 14, 57 (1965); Riv. Nuovo Cim. Speciale 252 (1969)

    Article  Google Scholar 

  15. Particle Data Group, K. Hagiwara et al. , Phys. Rev. D 66, 010001 (2002)

    Article  Google Scholar 

  16. The experimental values for the energy levels of the hydrogen and deuterium may be found in http://physics.nist.gov

  17. M. Lacombe, B. Loiseau, J.M. Richard, R. Vinh Mau, J. Côté, P. Pirés, R. de Tourreil, Phys. Rev. C 21, 861 (1980)

    CAS  Google Scholar 

  18. R.V. Reid, Jr., Ann. Phys. 50, 411 (1968)

    Article  Google Scholar 

  19. R.B. Wiringa, V.G. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)

    CAS  Google Scholar 

  20. M.R. Robilotta, Nucl. Phys. A 595, 171 (1995); M.R. Robilotta, C.A. Rocha, Nucl. Phys. A 615, 391 (1997); R. Higa, M.R. Robilotta, Phys. Rev. C 68, 024004 (2003)

    Article  Google Scholar 

  21. A. De Rújula, H. Georgi, S.L. Glashow, Phys. Rev. D 12, 147 (1975)

    Article  Google Scholar 

  22. S.N. Gupta, S.F. Radford, W.W. Repko, Phys. Rev. D 26, 3305 (1982)

    CAS  Google Scholar 

  23. J. Pantaleone, S.-H.H. Tye, Y.J. Ng, Phys. Rev. D 33, 777 (1986)

    CAS  Google Scholar 

  24. E. Eichten, F. Feinberg, Phys. Rev. D 23, 2724 (1981)

    CAS  Google Scholar 

  25. E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane, T.-M. Yan, Phys. Rev. 17, 3090 (1978); 21, 203 (1980)

    CAS  Google Scholar 

  26. P.N. Bogolioubov, Ann. Inst. Henri Poincaré 8, 163 (1967)

    Google Scholar 

  27. F.E. Close, An introduction to quarks and partons. Academic Press, London, 1979

  28. R. Tegen, Ann. Phys. 197, 439 (1990)

    CAS  Google Scholar 

  29. L.A. Trevisan, L. Tomio, Nucl. Phys. A 689, 485 (2001)

    Article  Google Scholar 

  30. P.L. Ferreira, J.A. Helayel, N. Zagury, Nuovo Cim. A 55, 215 (1980)

    Google Scholar 

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Authors and Affiliations

  1. Instituto de Física, Universidade de São Paulo, C.P. 66318, 05315-970 São Paulo, SP, Brazil

    C. C. Barros Jr.

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  1. C. C. Barros Jr.
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Correspondence to C. C. Barros Jr..

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Received: 27 January 2005, Revised: 15 April 2005, Published online: 31 May 2005

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Barros, C.C. Quantum mechanics in curved space-time. Eur. Phys. J. C 42, 119–126 (2005). https://doi.org/10.1140/epjc/s2005-02252-7

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  • DOI: https://doi.org/10.1140/epjc/s2005-02252-7

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