Can atomic processes be described by non-linear wave mechanics in space-time?

Ernest J. Sternglass

Daniel Crespin

The model of the hydrogen atom originally introduced by Erwin Schrödinger in 1926 isa two-body proton -electron system. It relies on the Schrödinger operator H and on thelinear Schr¨odinger time dependent equation. Then Niels Bohr discovered that the modelcontradicts the basic dynamics of the atom and quantum wave mechanics was invented,with incidences here told from a deconstructive standpoint. The final section of this papersketches a new, alternative, continuous, causal and fully deterministic wave mechanics—already mentioned in [1], [2], [3] and elsewhere— crucially relying on H and solvablein terms of its eigenvalues and eigenfunctions, but definitely non-linear. An importantimplication is that the deterministic hydrogen atom must be conceived as a three-bodysystem consisting of proton, electron and photon.

Kunming Xu

Euclidean space and linear algebra do not characterize dynamic electronic orbitals satisfactorily for even the motion of both electrons in an inert helium atom cannot be defined in reasonable details. Here the author puts forward a novel two-dimensional spacetime model from scratch in the context of defining both electrons in a helium atom. Space and time are treated as two orthogonal, symmetric and complementary quantities under the atomic spacetime. Electronic motion observed the rule of differential and integral operations that were implemented by dynamic trigonometric functions. It is demonstrated that the atomic spacetime is not a linear vector space with Newtonian time, and within which calculus has non-classical definition, and complex wave functions have fresh physical significances. This alternative approach is original, informative and refreshing but still compatible with quantum mechanics in the formulation. The description of electronic resonance in helium is also comparable with classical mechanics such as an oscillating pendulum and with classical electromagnetism such as an LC oscillator. The study has effectively unified complex function, calculus, and trigonometry in mathematics, and provided a prospect for unifying particle physics with classical physics on the novel spacetime platform.

É. Papp

George Birtwistle

Wave mechanics In the classical dynamics the state of the system whose coordinates are q 1 … q s and momenta p 1 … p s is denoted by a point in 2s-dimensional space (the q-space); changes in the system are indicated by the passage of the point along some curve in this space, a ‘ray,’ it may be called. Schrödinger's new concept is that changes in the system should be represented in the q-space not by ‘rays’ but by ‘waves.’ He regards the classical mechanics as only an approximation to actual mechanical events, which he says can only be described by wave mechanics; the former in his view bears to the latter just the same relation as geometrical (or ‘ray’) optics does to physical (or ‘wave’) optics. A large scale (macroscopic) mechanical process corresponds to a wave signal in the g-space, which can be regarded as a point in comparison with the geometrical structure of its path. But for small scale (microscopic) processes, such as atomic phenomena are, the rigorous wave theory must be used. The wave equation must replace the usual dynamical equations. The latter are just as unfruitful for the purposes of atom mechanics as geometrical optics alone would be to clear up the fine points of diffraction phenomena.