Quantum Laws in Connection with Stochastic Processes

Abstract

It is shown that, with :;uitable conventions, Schrodinger's equation can be deduced from the laws of stochastic diffusion; uncertainty relations, concrete meaning of mass-energy equivalence, minimal constants of time and length and vanishing of negative energy also appear resulting from the basic conventions. An extension to mechanics with spin is worked out, and a model of Dirac's fluid is elaborated. Stochastic assumptions also lead to the energy states and quantum numbers of the hydrogen atom. Suggestions are made on the physical interpretation of the moc'tei, on it:s relation to the wave-particle dualism, and on the meaning of quantized states. at Karolinska Institutet University Library on May 29, 2015 http://ptp.oxfordjournals.org/ Downloaded from >· 0) ( ·>' ~cj •"-·k (4) approach zero with t. (We shall occasionally have to admit similar relations for higher orders.) d) The fluid satisfies the equation of Fokker-Planck: *) *) The condition d) is a consequence of a)+ b) +c), if definite c~ndition wf continuity and con v~r gence arc fulfdlcd (see (T), chap. If, §:~). at Karolinska Institutet University Library on May 29, 2015 http://ptp.oxfordjournals.org/ Downloaded from fJ the mean time of' free travel, a 0 the mean velocity of free travel, A the mean free path. (None of these quantities is vanishing nor infinite.) *) Except if the collisions take place at an infinite clistance (see the following footnote).**) Unless non null contributions in ))·r• come from collisions at an infinite distance, but then the mean free path would be infinite.

Classical tunneling

“…There have been a number of quasiclassical approaches to quantum mechanics (utilizing mechanisms such as background fluctuations) in which the Schrödinger equation and the Klein-Gordon equation have been derived (Bohm, 1952;Aron, 1965Aron, , 1966Nelson, 1966;Lehr and Park, 1977;Park et al, 1980). Once this has been achieved, tunneling is introduced in the same way as in quantum mechanics with no classical insight as to how a body can get through a barrier when its energy is less than that of the barrier height.…”

Conceptual problems in quantum mechanics

“…В пользу этого соображения говорит тот факт, что соотношение (7.5) (см. ниже), являющееся следствием уравнения Шрёдингера, имеет такую же структуру, как и уравне ние диффузии [108,109], а именно, оно содержит первую производную по времени и вторую производную по координатам. Однако согласно этой модели энергия частиц, прошедших через потенциальный барьер, имела бы случай ный разброс -от нуля до высоты барьера, в то время как все вылетающие частицы имеют энергию, в точности равную 4,8 МэВ.…”