Quantum particle motion in physical space

Abstract

Using Feynman's representation of the quantum evolution and considering a quantum particle as a matter field (continuous medium), it is shown that individual particles of the field have unique paths of the motion. This allows describing motion of the quantum particle continuous medium by Lagrange's method. It is shown that form of the real individual particle path is determined by classical minimum action principle.

Nonlinear dynamics of open quantum systems

“…6 If the wave function of the particle is instantaneous localized under the position measurement, then Schrödinger's wave function interpretation "...as giving somehow the density of the stuff of which the world is made" [3] does not create the "problem of the wave packet spreading". 7 In addition to the specific properties of individual particles of such a continuous medium [20], its fundamental difference from the classical one is that individual particles of this continuum actually form an everywhere dense set in the volume accessible to a quantum particle (there is no empty space in it), whereas for a classical continuous medium, this property is a mathematical abstraction. When the measure density flux can be neglected, as, for example in the case of reduction process, change of the probability in a volume is possible if ∂S A ∂t = 0.…”

Quantum evolution as a usual mechanical motion of peculiar continua

“…The first property of the physical continuum is analogous to the classical one and consists in the fact that material points move in accordance with the principle of least action [5].…”

“…The actions in the last expression depend on arbitrary point in time in the past , which cancel in the continuity equation in the form (5). Then for the continuity equation in term of the complex density ( , ), we get…”

“…In general the active element consist of a set of elementary particles. Since, the size of an element is assume to be small compared to the spatial size Δ ∼ / , the active element can be considered as a quantum particle, whose position we denote by 5 . In the considered case, the active element is a composite continuous medium described by the function ( ), which differs from zero inside a much smaller spatial volume than the function ( ).…”