Generalized Lagrangian-path representation of non-relativistic quantum mechanics

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19240%2F16%3AN0000130" target="_blank" >RIV/47813059:19240/16:N0000130 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007%2Fs10701-016-9989-7" target="_blank" >https://link.springer.com/article/10.1007%2Fs10701-016-9989-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10701-016-9989-7" target="_blank" >10.1007/s10701-016-9989-7</a>

Result language

angličtina

Original language name

Generalized Lagrangian-path representation of non-relativistic quantum mechanics

Original language description

In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm “pilot-wave” interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the $N$-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton–Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in $1$- or $N$-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Foundations of Physics

ISSN

0015-9018

e-ISSN

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Volume of the periodical

46

Issue of the periodical within the volume

8

Country of publishing house

US - UNITED STATES

Number of pages

40

Pages from-to

1022-1061

UT code for WoS article

000379220800005

EID of the result in the Scopus database

2-s2.0-84977151050