A classical basis for quantum mechanics

We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization. 1 The neccessity of quantum mechanics (QM) was a result of experimental data for the energy spectrum of atoms which could not be explained in accord with the laws of classical mechanics. Nevertheless in the axiomatic basis of QM there are axioms which are not supported by the experimental results, since the whole system of axioms (1) is introduced only as a ”plausible generalization ” of the first axiom [1]:

F. Romanelli

R. Collins

Lin Cun-fan

In the paper, the second applicable range (macroscopic body) of classical mechanics is fulfilled as symmetrical and strict as the first applicable range (vc) on the basis of quantum mechanics. And another applicable range (application in body which is not acted as chaos movement) is presented on the basis of chaos theory.

M. Carioli, Eric J. Heller, Klaus B. Mo ller

The choice of basis states in quantum calculations can be influenced by several requirements, and sometimes a very natural basis suggests itself. However often one retreats to a “merely complete” basis, whose coefficients in the eigenstates carry little physical insight. We suggest here an optimal representation, based purely on classical mechanics. “Hidden” constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies the hierarchical structure of couplings between “zero-order” states. We present a (non-perturbative) method to obtain such a basis-state as solutions to a certain resonant Hamilton–Jacobi equation.

Alberto Galindo, P. Pascual