Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

Journal Article · Tue Sep 15 00:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.05.001· OSTI ID:22451208

Cruz, Hans ^[1]; Schuch, Dieter ^[2]; Castaños, Octavio ^[1]; Rosas-Ortiz, Oscar ^[3]

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1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico)
2. Institut für Theoretische Physik, JW Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany)
3. Physics Department, Cinvestav, A. P. 14-740, 07000 México D. F. (Mexico)

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

• OSTI ID: 22451208
• Journal Information: Annals of Physics, Vol. 360; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
HAMILTONIANS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM SYSTEMS
RICCATI EQUATION
WAVE PACKETS