On a Parallelism between Classical Mechanics and Quantum Mechanics

Mixing Quantum and Classical Mechanics

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of f...

A method for classical and quantum mechanics

In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods, which have been applied and developed practically in all areas of Physics. Unfortunately many interesting problems in Physics are of non-perturbative nature ...

The equivalence principle in classical mechanics and quantum mechanics ∗

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all. While the equiva...

Plain Mechanics: Classical and Quantum Mechanics as Well

This is the written version of a short talk on 10 Conference on Problems and Methods in Mathematical Physics (September 13 17, 1993 in Chemnitz, Germany). A new scheme of the quantization is presented. A realization of the scheme for a particle in n-dimensional space by two-sided convolutions on the Heisenberg group is constructed.

Classical models of quantum mechanics