Stationary States in the Relativistic Quantum Theory of Wave Fields

Isaac Shnaid

Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or multi-particle non-relativistic quantum system is initially in a stationary state, and its wave function field is locally perturbed, then perturbed and non-perturbed sub-regions appear in the region. According to Schrödinger equation, borders of the perturbed sub-region propagate with infinite speed, and the perturbation instantaneously affects all infinite region. It means that Schrödinger equation predicts infinite speed of the wave function perturbations propagation. This feature of classical Schrödinger equation is traditionally interpreted as non-locality of quantum mechanics. From physical point of view, such mathematical behavior of Schrödinger equation solutions is questionable because it is difficult to accept that in real world infinite physical objects can instantaneously appear. We introduce a hypothesis that in reality speed of propagation of the perturbed sub-region borders is equal speed of light. On this basis we develop and analyze a finite propagation speed concept for non-relativistic quantum equations. It leads to local interpretation of non-relativistic quantum mechanics consistent with principle of locality and free of local hidden variables. The theory is applied to analysis of Einstein-Podolsky-Rosen (EPR) paradox, entanglement and properties of perturbed matter waves. We proved that formulated theory agrees with results of classical experiments on electron matter waves diffraction.

Gerald Rosen

Piravonu Mathews Mathews, Kavitha Venkatesan

1. Towards Quantum Mechanics 2. The Schrodinger Equation and Stationary states 3. General Formalism of Wave Mechanics 4. Exactly Solvable Eigenvalue Problems 5. Approximation Methods for Stationary States 6. Scattering Theory 7. Representations, Transformations and Symmetries 8. Anguar Momentum 9. Evolution with Time 10. Relativistic Wave Equations

B.T. Geylikman

Gerald Rosen

For theories featuring n scalar fields and an interaction energy density that converges rapidly for large field magnitudes to the form representative of a linear theory, we present exact physical solutions to the Schrödinger stationary state equation. These solutions show that such quantum field theories are effectively linear with no interaction and scattering between the quanta.

W-Y. P. Hwang, Ta‐You Wu