Poincaré's 191112 proof of quantum discontinuity interpreted as applying to atoms
Abstract
As part of a study of Planck's blackbody radiation theory, H. Poincaré (in 191112) advanced a theory which analyzed the partition of energy between "resonators" and the kinetic motion of atoms. Resonators (the objects of Poincaré's theory) facilitate the exchange of energy between radiation and matter, but otherwise their identity has remained unresolved. Poincaré considered resonators characterized by a particular mean energy ɛ/[exp(ɛ/kT)1], which he showed to necessarily imply quantized energies nɛ (n=0,1,2,…). We additionally consider resonators characterized by a mean energy ɛ/[exp(ɛ/kT)+1], which (using Poincaré's methodology) we show to necessarily imply quantized energies nɛ (n=0 and 1). Resonators are here identified with transitions between internal quantum states of atoms. This includes normal electronic atoms characterized by possible energies nɛ (n=0 and 1), as well as atoms populated by subatomic bosons (such as pions) and characterized by multiple occupancy of quantum states and possible energies nɛ (n=0,1,2,…). We distinguish between Poincaré's theory and the closely related analysis by P. Ehrenfest of quantization amongst cavity modes.
 Publication:

American Journal of Physics
 Pub Date:
 August 2001
 DOI:
 10.1119/1.1356056
 Bibcode:
 2001AmJPh..69..879I
 Keywords:

 01.50.i;
 03.65.Ge;
 03.65.Sq;
 31.10.+z;
 44.40.+a;
 36.10.Gv;
 Educational aids;
 Solutions of wave equations: bound states;
 Semiclassical theories and applications;
 Theory of electronic structure electronic transitions and chemical binding;
 Thermal radiation;
 Mesonic atoms and molecules hyperonic atoms and molecules