An Alternative Approach to Wave Mechanics of A Particle at the Non-Relativistic Approximation

  • Augustin Blaquière
  • Angelo Marzollo
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 294)


The mathematical theory of stochastic dynamic programming has cast a new light on the conceptual foundation of wave mechanics [1]. In this chapter we shall return to an illustration of that point of view, and more specifically to section 5 of the paper by Blaquière and Marzollo, published in [2]. Recently we have been aware, thanks to J.C. Zambrini, of an article by Schrödinger published in 1932 [3], in which a model identical with ours was presented as a possible starting point for an alternative approach to wave mechanics.


Grad Versus Wave Mechanic Stochastic Dynamic Programming Stochastic Control Problem Optimal Stochastic Control Problem 
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    Blaquière, A., System Theory: A New Approach to Wave Mechanics, Journal of Optimization Theory and Applications, Vol.32, N°4, 1980.CrossRefGoogle Scholar
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    Blaquière, A., Marzollo, A., Introduction à la théorie moderne de l’optimisation et à certains de ses aspects fondamentaux an physique, In La pensée physique contemporaine, Edts., S. Diner, D. Fargue, G. Lochak, Editions Augustin Fresnel, 1982.Google Scholar
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    Schrödinger, E., Une analogie entre la mécanique ondulatoire et quelques problèmes de probabilités en physique classique, Annales de l’Institut Henri Poincaré, 1932.Google Scholar
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    Dreyfus, S.E., Dynamic Programming and the Calculus of Variations, Academic Press, New York, 1965.MATHGoogle Scholar
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    De Broglie, L., Line tentative d’interpretation causale et non-linéaire de la mécanique ondulatoire, Gauthier-villars, Paris, 1956.Google Scholar

Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • Augustin Blaquière
    • 1
  • Angelo Marzollo
    • 1
  1. 1.Université de Paris VIIParisFrance

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