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...

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...

Classical models of quantum mechanics