Euler & Lagrange versus Heisenberg & Schroedinger: Dynamical Pictures in Classical and Quantum Mechanics
@article{Partovi2013EulerL,
title={Euler \& Lagrange versus Heisenberg \& Schroedinger: Dynamical Pictures in Classical and Quantum Mechanics},
author={M. Hossein Partovi},
journal={arXiv: Quantum Physics},
year={2013}
}Using quantum-classical analogies, we find that dynamical pictures of quantum mechanics have precise counterparts in classical mechanics. In particular, the Eulerian and Lagrangian descriptions of fluid dynamics in classical mechanics are the analogs of the Schroedinger and Heisenberg pictures in quantum mechanics, respectively. Similarities between classical and quantum dynamical pictures are explored within the framework of the Koopman-von Neumann formalism. These allow for a natural…
References
SHOWING 1-10 OF 17 REFERENCES
The S Matrix in Quantum Electrodynamics
- Physics
- 1949
The covariant quantum electrodynamics of Tomonaga, Schwinger, and Feynman is used as the basis for a general treatment of scattering problems involving electrons, positrons, and photons. Scattering…
Ergodic theory of chaos and strange attractors
- Physics
- 1985
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the…
Absence of sensitivity to initial conditions in quantum dynamics.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992
It is shown, under very general conditions, that there exists no positive characteristic exponent nor any sensitivity to initial conditions, however weak, in quantum dynamics, which implies the nonexistence of chaos is quantum mechanics.
A quantum-theoretical reinterpretation of kinematic and mechanical relations
- Physics
- 1925
In der Arbeit soll versucht werden, Grundlagen zu gewinnen fur eine quantentheoretische Mechanik, die ausschlieslich auf Beziehungen zwischen prinzipiell beobachtbaren Grosen basiert ist.
Algorithmic complexity and randomness
- Computer Science
- 2001
This presentation will provide an introduction to the basic ideas of algorithmic complexity and randomness, as well to the applications of these ideas to the characterization of dynamical systems as examples of complex behavior.
On the Length of Programs for Computing Finite Binary Sequences
- Computer ScienceJACM
- 1966
An application to the problem of defining a patternless sequence is proposed in terms of the concepts here developed to study the use of Turing machines for calculating finite binary sequences.