Nonlinear quantum mechanics: Results and open questions

Journal Article · Thu May 15 04:00:00 EDT 2008 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778808050177· OSTI ID:21402580

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schroedinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.

• OSTI ID: 21402580
• Journal Information: Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 5 Vol. 71; ISSN 1063-7788; ISSN PANUEO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CURRENT ALGEBRA
DIFFERENTIAL EQUATIONS
DISTURBANCES
EQUATIONS
EVOLUTION
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MATHEMATICAL EVOLUTION
MECHANICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SPACE
SYMMETRY
TIME DEPENDENCE
WAVE EQUATIONS