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Modern Physics Letters B

THE QUASICLASSICAL LOCALIZATION OF THE STATES AND OBTAINING OF CLASSICAL EQUATIONS OF MOTION FROM QUANTUM THEORY

Vladislav G. Bagrov, Владимир Владимирович Белов, A. M. Rogova, Andrey Yu. Trifonov

Published Nov 10, 1993• 11 citations
Publisher

Abstract

The concept of quasiclassically localized states is defined and the theorem about the possibility of the quasiclassical localization on the phase trajectories only (solutions of corresponding classical equations of Hamilton) is proved.
DOI
10.1142/s0217984993001703

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На основе квазиклассического подхода в рамках квантовой механики предлагается классическая интерпретация движения электрона в атоме в его sсостоянии как движение по радиальным линиям с возможностью туннельного перехода сквозь ядро и изменением направления движения в результате столкновений с кварками ядра. Based on a quasiclassical approach within the framework of quantum mechanics, we propose a classical interpretation of the electron motion in an atom in its sstate as a motion along radial lines with the possibility of tunneling through the nucleus and changing the direction of motion as a result of collisions with the nuclei quarks.
In this paper we show that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation, such that the quantum-mechanical averages of the coordinates and the momenta with respect to these states are general exact solutions of the classical Hamiltonian equations. Such states are called trajectory-coherent states. The wave functions of the trajectory-coherent states are obtained by the complex germ method by V. P. Maslov. The simplest properties of these states are studied.
When dealing with macroscopic objects one usually observes quasiclassical phenomena, which can be described in terms of quasiclassical (or classical) equations of motion. Recent development of the theory of quantum computation is based on implementation of the entangled states which do not have a classical analogy. Using a simple example of a paramagnetic spin system we show that the entangled states can be detected in standard macroscopic experiments as a sharp deviation from quasiclassical motion.