The Relation Between Classical and Quantum Mechanics

Relation between classical and quantum particle systems.

An exact correspondence is established between a N-body classical interacting system and a (N-1)-body quantum system with respect to the partition function. The resulting Hermitian quantum potential is a (N-1)-body one. Inversely the Kelbg potential is reproduced which describes quantum systems at a quasi-classical level. The correspondence found between classical and quantum systems allows als...

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...

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...

Relation to Quantum Mechanics

Classical Limit of Quantum Mechanics

para o valor esperado de uma dada observável fı́sica A = A(p, q, t) representada pelo operador Â. As equações (1) e (2) são válidas desde que o potencial externo V varie vagarosamente dentro de um pacote de onda bem localizadoψPE (Pacote de Ehrenfest). Assim, de acordo com os livros-texto [1], as equações de Newton são obtidas como limite clássico da equação de Schrödinger. No entanto, Ballentin...