Classical physics foundations for quantum physics

We employ classical principles to justify various quantum concepts. Among these are (1) the Planck formula for the energy of a photon, (2) the de Broglie relation, (3) the Schrodinger energy and momentum operators, (4) the position-momentum commutator relation and (5) the Schrodinger wave function. Thus for the Planck formula we require only basic thermodynamics, the Doppler effect and the assumption that photons esist. The de Broglie relation results from the quantization of action combined with the hypothesis of the existence of de Broglie waves and the properties of standing waves. Items (3) and (4) are direct consequences of classical definitions of action in terms of energy and/or momentum, the existence of a unit of action, and the use of the function of action phi(S) = exp(iS/(h) over bar), where S is the action. The wave function stems, in addition, from the inability to assign a particle to a precise classical path having a definite action; instead, we must have a bundle of paths, of varying action, which differ from each other by no more than the unit of action. The sum over these paths yields the wave function.