A simple derivation of the Schroedinger equation from the theory of Markoff processes

J. Fronteau

E. Onofri

L. de la Peña-Auerbach, L. S. Garcı́a-Colı́n

SUMMARY 1967 In tbis paper a derivation of a genera/iud Schroedinger equation va lid lar velocity dependent forces. is presented. The physical assumptions invo/ved rest on the hypothesis that a more general quantum mechanical description of a partie/e may be constructed if we sJart from a Markoff process as described by FokkerPianck's equation in phase space. lt is also shown that Ihe asymptotic limil kads to the ardinary formalism of quantum mechanics in configuralion space togelher wilh a new equation in velocily space which al/ows us lo generate quanlum numbers which are tentatively associated with SOme of those characleristic ollhe portie/e. This formulation leads to a lirst es tima te ollbe parameler j3 introduc('d in pr(' vious papers. Consultont. Comision Nacional de Energia Nudear (Mexico).

Mário J. de Oliveira

H. N. Ioannidou

Andrei P. Kirilyuk

Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed, at the beginning of 1926, the concept of wavefunction and wave equation for it. Though endowed with a realistic undular interpretation by its father, the wavefunction could not be considered as a real "matter wave" and has been provided with only abstract, formally probabilistic interpretation. In this paper we show how the resulting "mysteries" of usual theory are solved within the unreduced, dynamically multivalued description of the underlying, essentially nonlinear interaction process (quant-ph/9902015, quant-ph/9902016), without artificial modification of the Schroedinger equation. The latter is rigorously derived instead as universal expression of unreduced interaction complexity. Causal, totally realistic wavefunction is obtained as a dynamically probabilistic intermediate state of a simple system with interaction performing dynamically discrete transitions between its localised, incompatible "realisations" ("corpuscular" states). Causal wavefunction and Schroedinger equation are then extended to arbitrary level of world dynamics. We outline some applications of the obtained causal description, such as genuine quantum chaos (quant-ph/9511034-36) and realistic quantum devices (physics/0211071), and emphasize the basic difference of the proposed dynamically multivalued theory from dynamically single-valued imitations of causality and complexity. The causally complete wavefunction concept, representing the unified essence of unreduced (multivalued) complex dynamics, provides a clear distinctive feature of realistic science, absent in any its unitary imitation.