Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles

Journal Article · Mon May 15 00:00:00 EDT 2017 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2017.03.002· OSTI ID:22617500

Gonçalves, L. A.; Olavo, L. S.F.,

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.

• OSTI ID: 22617500
• Journal Information: Annals of Physics, Vol. 380; Other Information: Copyright (c) 2017 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
CLASSICAL MECHANICS
HAMILTONIANS
QUANTIZATION
QUANTUM MECHANICS
SCHROEDINGER EQUATION