Title: On the unique mapping relationship between initial and final quantum states

In its standard formulation, quantum mechanics presents a very serious inconvenience: given a quantum system, there is no possibility at all to unambiguously (causally) connect a particular feature of its final state with some specific section of its initial state. This constitutes a practical limitation, for example, in numerical analyses of quantum systems, which often make necessary the use of some extra assistance from classical methodologies. Here it is shown how the Bohmian formulation of quantum mechanics removes the ambiguity of quantum mechanics, providing a consistent and clear answer to such a question without abandoning the quantum framework. More specifically, this formulation allows to define probability tubes, along which the enclosed probability keeps constant in time all the way through as the system evolves in configuration space. These tubes have the interesting property that once their boundary is defined at a given time, they are uniquely defined at any time. As a consequence, it is possible to determine final restricted (or partial) probabilities directly from localized sets of (Bohmian) initial conditions on the system initial state. Here, these facts are illustrated by means of two simple yet physically insightful numerical examples: tunneling transmission and grating diffraction. -- Highlights: •The conceptmore » of quantum probability tube is introduced. •Quantum tubes result from the evolution of a separatrix set of initial Bohmian conditions. •Probabilities inside these sets remain constant along the corresponding quantum tubes. •Particular features of final states are then uniquely linked to specific regions of initial states. •Tunneling and grating diffraction are analyzed.« less

Instituto de Física Fundamental (IFF–CSIC), Serrano 123, 28006 Madrid (Spain)

(United Kingdom)

Publication Date:

OSTI Identifier:

22224245

Resource Type:

Journal Article

Resource Relation:

Journal Name: Annals of Physics (New York); Journal Volume: 339; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CURRENT DENSITY; DIFFRACTION; EVOLUTION; GRATINGS; MAPPING; NUMERICAL ANALYSIS; PROBABILITY; QUANTUM MECHANICS; QUANTUM STATES; SPACE; STANDARDS; TRANSMISSION; TUNNEL EFFECT