From classical Hamiltonian flow to quantum theory: Derivation of the Schrödinger equation

Foundations of Physics Letters

Volumn 17, Issue 4, 2004, Pages 343-362

  Grössing, Gerhard ^a  

^a Austrian Institute for Nonlinear Studies Vienna   (Austria)

Author keywords

classical Hamiltonian flow; Schr dinger equation

Indexed keywords

EID: 4043095457     PISSN: 08949875     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:FOPL.0000035669.03595.ce     Document Type: Article

References (18)

1. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1950).
2. P. R. Holland, "Electromagnetism, particles and anholonomy," Phys. Lett. A 91 (1982), 275-278.
3. E. Schrödinger, "Unsere Vorstellung von der Materie" (1952), in E. Schrödinger, Was ist Materie?, Audio CD-ROM, Köln, 2002 (our translation).
4. S. A. Werner, R. Clothier, H. Kaiser, H. Rauch, and H. Wölwitsch, "Spectral filtering in neutron interferometry," Phys. Rev. Lett. 67 (1991), 683-687.
5. D. L. Jacobson, S. A. Werner, and H. Rauch, "Spectral modulation and squeezing at high-order neutron interferences," Phys. Rev. A. 49 (1994), 3196-3200.
6. M. J. W. Hall and M. Reginatto, "Schrödinger equation from an exact uncertainty principle," J. Phys. A 35 (2002), 3289-3303.
7. R. J. Harvey, "Navier-Stokes analog of quantum mechanics," Phys. Rev. 152 (1966), 1115.
8. D. Bohm, "A suggested interpretation of the quantum theory in terms of 'hidden variables'," I and II, Phys. Rev. 85 (1952), 166-179, 180-193.
9. P. R. Holland, The Quantum Theory of Motion (University Press, Cambridge, 1993).
10. R. A. Fisher, "Theory of statistical information," Phil. Trans. Roy. Soc. London, Ser. A 222 (1930), 309-368.
11. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
12. B.-G. Englert, M. O. Scully, and H. Walther, "Complementarity and uncertainty," Nature 375 (1995), 367.
13. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II (Addison-Wesley, Reading, MA, 1965), Chap. 40-2.
14. E. Nelson, Quantum Fluctuations (University Press, Princeton, 1985).
15. P. Garbaczewski, "Noise perturbations in the Brownian motion and quantum dynamics," Phys. Lett. A 257 (1999), 31-36.
16. G. Grössing, Quantum Cybernetics. Toward a Unification of Relativity and Quantum Theory via Circularly Causal Modeling (Springer, New York, 2000).
17. G. Grössing, "Quantum cybernetics: A new perspective for Nelson's stochastic theory, nonlocality, and the Klein-Gordon equation," Phys. Lett. A 196, 1 (2002), 1-8.
18. R. S. Mulliken, "The band spectrum of boron monoxide," Nature 114 (1924), 349-350. This paper is usually considered as reporting the first empirical evidence of the reality of the zero-point energy; many others were to follow. Note that the paper appeared well before the advent of the complete formulation of modern quantum theory.