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arXiv:0904.0960 · Bulletin of the American Physical Society

Principles and Dynamics of Quantum Mechanics

Spyros Efthimiades

Published Apr 6, 2009• 0 citations
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Abstract

The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction is described by a potential, the total energy of the particle is equal to its total kinetic plus potential energies. We derive the Schrodinger and Dirac equations as the conditions the wavefunction must satisfy at each point in order to fulfill the corresponding energy equation. In our approach quantum theory is tangible, experimentally justified and theoretically consistent. PACS numbers: 03.65.-w Keywords: Quantum principles; Quantum dynamics; Schrodinger equation; Dirac equation

DOI
10.48550/arxiv.0904.0960

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The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction is described by a potential, the total energy of the particle is equal to its total kinetic plus potential energies. We derive the Schrodinger and Dirac equations as the conditions the wavefunction must satisfy at each point in order to fulfill the corresponding energy equation. In our approach quantum theory is tangible, experimentally justified and theoretically consistent. PACS numbers: 03.65.-w Keywords: Quantum principles; Quantum dynamics; Schrodinger equation; Dirac equation
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total kinetic plus potential energies. We derive the Schrodinger and Dirac equations as the unique conditions the wavefunction must satisfy at each point in order to fulfill the corresponding energy equation. PACS numbers: 03.65.-w. Keywords: Schrodinger equation; Dirac equation; Quantum dynamics.
We determine that the wavefunction of an interacting particle is the superposition of its virtual concurrent states. In many cases we can tell what concurrent states arise. Furthermore, we derive the Schrodinger and Dirac equations as the unique conditions the wavefunction must satisfy at each point in order to fulfill the corresponding averaged energy relation. In the balanced particle state and wave approach we follow, quantum dynamics becomes tangible and we obtain a logically connected and physically justified quantum theory.
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation cannot be a physical postulate, and we show that the heuristic derivations wrongly consider that the particle kinetic energy is proportional to the square of the momentum operator acting on the wavefunction. The correct term is proportional to the square of the momentum. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. As a result, quantum mechanics becomes a local and global theory, while in the traditional formulation it is a local theory. In several interaction settings we can tell what particle motions arise and explain the outcomes in simple and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.
The one-particle Schrödinger and Dirac equations are derived, without making any quantization hypothesis, from the postulate that an elementary particle is a physical wave packet of dynamically varying form and size, rather than a pointlike object located somewhere within the support of a wavefunction that serves only as a mathematical probability amplitude. An isolated multiparticle system can, similarly, be described in principle as a set of interacting wave packets governed by coupled one-particle equations, a picture from which, in the nonrelativistic limit, the multiparticle Schrödinger equation can be obtained as a sufficiency condition for the system to have a conserved total energy equal to a particular value E .
Quantum mechanics is based on the concepts of indeterminacy , indistinguishability probability amplitudes , probabilities , reversibility , superposition , and uncertainty . And yet that is only part of the essence of quantum mechanics. Using the words attached to the concepts just described provides only a partial description of what quantum mechanics really is. The other part is provided by a set of physical and mathematical principles annexed to the mentioned concepts. The beauty is that quantum mechanics becomes workable and functional just by observing its mathematical principles. There is no need for any particular interpretation. Not even the orthodox interpretation. Here, fifteen mathematical-physical principles of quantum mechanics are listed and succinctly explained.
The Schrödinger equation is the fundamental equation of quantum mechanics. Since its discovery in 1926, it has been postulated — accepted as a starting point whose origin remains unexplained. This paper derives it. The derivation begins not with physics but with three conditions that any coherent structure must satisfy in order to exist at all: (i) it must be self-consistent (identity), (ii) it must be capable of persisting through change (temporality), and (iii) it must be distinguishable from its environment (distinction). These three conditions are not physical laws; they are preconditions for anything — a particle, a field, a living organism — to be a definite, persisting, identifiable entity. From these three conditions alone, a unique dynamics on the space of all logically possible configurations can be derived. This dynamics takes the form of a probability flow with exactly three components. The first is a drift that pushes the system toward self-consistent configurations — states in which no internal contradictions remain. The second is a diffusion that prevents the system from collapsing to a single rigid state, maintaining the openness and fluctuation that characterize quantum systems. The third is a circulation — a closed, non-dissipative flow that neither creates nor destroys probability but moves it in loops. This circulation is the origin of time.