Classical dynamics and the Schrödinger theory

Leon Bess

S. Rupp, M. Sorg

Within the framework of Relativistic Schrodinger Theory (RST), the static two-particle solutions of the RST dynamics in an external binding force field (Coulomb potential) are studied in detail. The typical quantum effects occurring in bound two-particle systems (such as particle indistinguishability, entanglement, and ortho-para splitting of the energy levels) turn out to be implications of the RST dynamics itself, not implications of an additional (anti-)symmetrization postulate as in the conventional quantum theory. The RST lowest-order approximations for the 2-particle energy levels are closer to the experimental values than the corresponding predictions of the conventional theory by (roughly) one order of magnitude.

Alexey A. Kryukov

Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. The Newtonian dynamics was shown to be the Schrodinger dynamics of states constrained to a submanifold of the space of states, identified with the classical phase space of the system. Quantum observables are identified with vector fields on the space of states. The commutators of observables are expressed through the curvature of the space. The resulting embedding of the Newtonian and Schrodinger dynamics into a unified geometric framework is rigid in the sense that the Schrodinger dynamics is a unique extension of the Newtonian one. Furthermore, under the embedding, the normal distribution of measurement results associated with a classical measurement implies the Born rule for the probability of transition of quantum states. In this paper, the implications of the obtained theory to the process of measurement in quantum theory are analyzed. The double-slit, EPR and Schrodinger cat type experiments are reviewed anew. It is shown that, despite reproducing the usual results of quantum theory, the framework is not simply a reformulation of the theory. New experiments to discover the predicted effects are proposed.

Maciej Zworski

Viraht Sahni

ABSTRACT According to the Bohr correspondence principle, the external temporal scalar potential in the classical equation of motion is replicated in quantum theory as a multiplicative operator. An equivalent quantum‐mechanical definition of the scalar potential in Schrödinger‐Pauli/Schrödinger theory is provided. The potential is a known universal functional of the wave function. At each instant of time, it is the work done in a conservative “classical” field representative of internal properties of the system: Pauli and Coulomb correlations, kinetic effects, the density, the Lorentz force, an internal magnetic component, and the current density response. The Hamiltonians are thus rewritten in a new physical manner indicative of these properties. An application to the triplet state of a 2‐electron semiconductor quantum dot in a magnetic field is provided. The significance of the definition to the Hohenberg‐Kohn theorem, and its relationship to Quantum and Kohn‐Sham density functional theory, is discussed.