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A POSSIBLE GENERALIZATION OF THE SCHRÖDINGER EQUATION BASED ON THE GAUSS PRINCIPLE OF LEAST SQUARES

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Foundations of Physics Letters

Abstract

The linear Schrödinger equation is generalized into non-linear equation based on the Gauss' principle of least squares. The weight function is assigned in such a way that it might be interpreted as occupation number density of hidden particles that obey the Fermi–Dirac stastistics. It is shown that the motion of a free particle, according to the so generalized non-linear equation, is described by a well behaved nondeforming wave packet moving with a constant velocity, in contrast to the always deforming wave packet according to the linear Schrödinger equation.

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REFERENCES

  1. L. de Broglie, Non-Linear Wave Mechanics (Elsevier, Amsterdam, 1960).

    MATH  Google Scholar 

  2. E. Schrödinger, “Der stetige Übergang von der Mikro-zur-Makro mechanik,” Naturwiss. 14, 664-666 (1926).

    Article  ADS  MATH  Google Scholar 

  3. S. Howard and S. K. Roy, “Coherent states of a harmonic oscillator,” Am. J. Phys. 55, 1109-1117 (1987).

    Article  ADS  Google Scholar 

  4. W. M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states theory and some applications,” Rev. Mod. Phys. 62 867-927 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  5. D. F. Styer, “The motion of wave packects through their expectation values and uncertainties,” Am. J. Phys. 58 742-744 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  6. C. C. Yan, “Soliton-like solutions of the Schrödinger equation for simple harmonic oscillator,” Am. J. Phys. 62 147-151 (1994).

    Article  ADS  Google Scholar 

  7. D. Bohm, “A suggested interpretation of the quantum theory in terms of 'hidden' variables I,” Phys. Rev. 85, 166-179 (1952); “A suggested interpretation of the quantum theory in terms of 'hidden' variables II,” Phys. Rev. 85, 180–193 (1952).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. A. C. Scott, F. Y. Y. Chu, and D. W. McLaughlin, “The soliton: A new concept in applied sciences,” Proc. IEEE 61, 1443-1483 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  9. L. D. Faddeev and L. A. Takhtajan, Harniltonian Methods in the Theory of Soliton (Springer, Berlin, 1987).

    Book  Google Scholar 

  10. B. Mielnik, “Generalized quantum mechanics,” Commun. Math. Phys. 37, 221-256 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  11. I. Bialynick-Birula and J. Mycielski, “Nonlinear wave mechanics,” Ann. Phys. 100, 62-93 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  12. R. Haag and U. Bannier, “Comments on Mielnik's generalized (non-linear) quantum mechanics,” Commun. Math. Phys. 60, 1-6 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  13. T. W. B. Kibble, “Relativistic models of nonlinear quantum mechanics,” Commun. Math. Phys. 64, 73-82 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  14. S. Weinberg, “Testing quantum mechanics,” Ann. Phys. 194, 336-386 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  15. C. C. Yan, “Hamilton's principle and Schrödinger's equation derived from Gauss' principle of of least squares,” Found. Phys. Lett. 13, 79-87 (2000).

    Article  MathSciNet  Google Scholar 

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  1. Instituto de Física, Universidade Federal do Rio de Janeiro, Ilha do Fundão, Rio de Janeiro, RJ, Brasil

    C. C. Yan

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  1. C. C. Yan
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Yan, C.C. A POSSIBLE GENERALIZATION OF THE SCHRÖDINGER EQUATION BASED ON THE GAUSS PRINCIPLE OF LEAST SQUARES. Found Phys Lett 13, 369–378 (2000). https://doi.org/10.1023/A:1007823728164

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