Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Adding dissipation to the Schrödinger equation from the quantum-potential viewpoint

Abstract

We discuss methods of adding dissipation to the Schrödinger equation in light of the quantum-potential interpretation of quantum mechanics. This favors nonlinear equations in general and Kostin's Schrödinger-Langevin equation in particular. We give a simple example, the damping of small coherent oscillations.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    T. P. Spiller, T. D. Clark, R. J. Prance, H. Prance, and D. A. Poulton,Nuovo Cimento 105B, 749 (1990).

  2. 2.

    T. P. Spiller, J. F. Ralph, T. D. Clark, R. J. Prance, and H. Prance,Phys. Lett. 244B, 333 (1990).

  3. 3.

    E.g., L. de Broglie, inRapport au V e Congres de Physique Solvay (Gauthier-Villars, Paris, 1930).

  4. 4.

    D. Bohm,Phys. Rev. 85, 166, 180 (1952).

  5. 5.

    For a recent review, see D. Bohm, B. J. Hiley, and P. N. Kaloyerou,Phys. Rep. 144, 321 (1987).

  6. 6.

    R. P. Feynman and F. L. Vernon Jr.,Ann. Phys. 24, 118 (1963).

  7. 7.

    A. O. Caldeira and A. J. Leggett,Phys. Rev. Lett 46, 211 (1981).

  8. 8.

    A. O. Caldeira and A. J. Leggett,Ann. Phys. 149, 374 (1983).

  9. 9.

    G. W. Ford, M. Kac, and P. Mazur,J. Math. Phys. 6, 504 (1965).

  10. 10.

    J. Ellis, S. Mohanty, and D. V. Nanopoulos,Phys. Lett. B221, 113 (1989).

  11. 11.

    J. Ellis, S. Mohanty, and D. V. Nanopoulos,Phys. Lett. B235, 305 (1990).

  12. 12.

    E.g. H. Goldstein,Classical Mechanics (Addison-Wesley, Reading, 1978), Chap. 9.

  13. 13.

    D. Bohm and B. J. Hiley,Phys. Rev. Lett. 55, 2511 (1985).

  14. 14.

    For a detailed discussion of these points, see Refs. 4 and 5.

  15. 15.

    H. Bateman,Phys. Rev. 38, 815 (1931), considered the damped oscillator problem.

  16. 16.

    P. Caldirola,Nuovo Cimento 18, 393 (1941).

  17. 17.

    E. Kanai,Prog. Theor. Phys. 3, 140 (1948).

  18. 18.

    H. Dekker,Phys. Rep. 80, 1 (1981).

  19. 19.

    P. Caldirola,Nuovo Cimento 77B, 241 (1983).

  20. 20.

    V. V. Dodonov and V. I. Manko,Nuovo Cimento 44B, 265 (1978);Phys. Rev. A20, 550 (1979).

  21. 21.

    I. R. Senitzky,Phys. Rev. 119, 670 (1960).

  22. 22.

    D. Greenberger,J. Math. Phys. 20, 762 (1979).

  23. 23.

    J. M. Cervero and J. Villarroel,J. Phys. A17, 2963 (1984).

  24. 24.

    R. W. Hasse,J. Math. Phys. 16, 2005 (1975).

  25. 25.

    W. E. Brittin,Phys. Rev. 77, 396 (1950).

  26. 26.

    P. Havas,Bull. Am. Phys. Soc. 1, 337 (1956);Nuovo Cimento Supp. 3, 363 (1957).

  27. 27.

    R. K. Colegrave and M. S. Abdalla,J. Phys. A14, 2269 (1981).

  28. 28.

    P. G. L. Leach,J. Phys. A16, 3261 (1983).

  29. 29.

    M. D. Kostin,J. Chem. Phys. 57, 3589 (1972).

  30. 30.

    K. K. Kan and J. J. Griffin,Phys. Lett. 50B, 241 (1974).

  31. 31.

    E. Madelung,Z. Phys. 40, 332 (1926).

  32. 32.

    M. D. Kostin,J. Stat. Phys. 12, 145 (1975).

  33. 33.

    K. Albrecht,Phys. Lett. B56, 127 (1975).

  34. 34.

    A. Davidson,Phys. Rev. A41, 3395 (1990).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Spiller, T.P., Spencer, P.S., Clark, T.D. et al. Adding dissipation to the Schrödinger equation from the quantum-potential viewpoint. Found Phys Lett 4, 507–521 (1991). https://doi.org/10.1007/BF00689888

Download citation

Key words

  • quantum potential
  • Schrödinger picture
  • dissipation
  • environment
  • coherence
  • damping