Abstract Real Wave Quantum Mechanics (RWQM) shows that quantum wave functions can arise naturally from the interaction of acoustic waves in an underlying medium, provided these exhibit a small degree of nonlinearity characterized by a dimensionless number, α. Small vortices called Field Rotators (FRs) containing angular momentum can form where there is a correlation between the phase of incoming waves and their direction of arrival. Interaction between FRs arranged in grids in a stochastic wave field can lead to self-sustaining structures which can be interpreted as charged leptons. FRs within the structures are described by their phase, amplitude and spin, thus mapping onto the wave functions of quantum mechanics. Calculations of small stationary state models in 1, 2 and 3 dimensions agree well with Schrödinger wave functions, except that the phases of neighbouring FRs alternate by π radians, a fact which is shown to be essential to the agreement and leads to the Pauli Exclusion Principle. Stable structures have internal phase variation not predicted by the Schrödinger equation, which is associated with internal energy flow and is lost when taking ψ∗ψ. It is hypothesized that orbital ’motion’ is a similar energy flow. Motion of whole structures through the medium leads directly to Special Relativity. The theory illuminates many ’difficult’ features of Quantum Mechanics. Quantitative confirmation of the theory is computationally difficult because of the huge number of interactions involved.
Abstract Real Wave Quantum Mechanics (RWQM) shows that quantum wave functions can arise naturally from the interaction of acoustic waves in an underlying medium, provided these exhibit a small degree of nonlinearity characterized by a dimensionless number, α. Small vortices called Field Rotators (FRs) containing angular momentum can form where there is a correlation between the phase of incoming waves and their direction of arrival. Interaction between FRs arranged in grids in a stochastic wave field can lead to self-sustaining structures which can be interpreted as charged leptons. FRs within the structures are described by their phase, amplitude and spin, thus mapping onto the wave functions of quantum mechanics. Calculations of small stationary state models in 1, 2 and 3 dimensions agree well with Schrödinger wave functions, except that the phases of neighbouring FRs alternate by π radians, a fact which is shown to be essential to the agreement and leads to the Pauli Exclusion Principle. Stable structures have internal phase variation not predicted by the Schrödinger equation, which is associated with internal energy flow and is lost when taking ψ∗ψ. It is hypothesized that orbital ’motion’ is a similar energy flow. Motion of whole structures through the medium leads directly to Special Relativity. The theory illuminates many ’difficult’ features of Quantum Mechanics. Quantitative confirmation of the theory is computationally difficult because of the huge number of interactions involved.
Self Interacting Wave Field (SIWF) theory replaces the ’probability wave’ interpretation of quantum mechanics with a mass-density one. It postulates the existence of a universal acoustic wave-bearing medium in Absolute Euclidian Space Time (AEST). Places where monochromatic waves arrive with phase and direction correlated have angular momentum and are called Field Rotators (FRs). Any non-linearity at FRs makes interaction between ’structures’ of FRs possible. Fundamental particles of nature arise from stable structures: where radiative losses are balanced against gains from resonance with a stochastic field within the medium. ’Phase Harmony’ within the structures has Special Relativity as a consequence. The de Broglie-Einstein equations hold if FRs rotate at the Compton frequency. Schrodinger’s wave function is shown to be a partial representation of the physical wave characterizing the motion of structures. Orbital and spin angular momenta are predicted to be ¯h and ¯h/2 respectively. The Pauli Exclusion principle is demonstrated. When applied to a 1-dimensional Simple Harmonic Oscillator and various square well potentials, the predicted eigenfunctions replicate those found via the Schrodinger equation. Eigenenergies also match if a dimensionless fractional parameter, α, is set to 1/π. In 3-D this could relate to the Fine Structure Constant.
Real Wave Quantum Mechanics (RWQM) seeks to demonstrate that standard Quantum Mechanics (QM) can be derived from first principles based entirely on the interactions of real waves in an underlying universal medium. This paper extends previous work on 1 and 2 dimensional applications which used discrete linear/grid structures of entities known as Field Rotators (FRs). It is shown that FRs can be extended continuously in the 3rd dimension to give threadlike forms named FReds. Although continuous, it is shown that the 3rd dimension can be discretized to simplify calculations. Results are similar to those from Schr\"odinger's equation and can be viewed interactively from within the document or directly from the Zenodo site by downloading the appropriate html file. The meaning and role of phase in standard QM is made clear and intuitive by the RWQM approach.
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical and high energy physics), the probabilistic interpretation of the Schroedinger wave ψ-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, the passage to the so-called operators of physical values, etc. Orthodox quantum mechanics was constructed as a physical theory developed in the phase space of the mentioned notions. That is why the formalism of quantum mechanics is aimed only at detailed calculations of the stationary states of the energy of the quantum system studied and is not able to describe a real path running by the system in the real space; instead, the formalism gives an averaged probabilistic prediction. Thus, if we are able to develop quantum mechanics in the real space, an option to clarify all the difficulties associated with the above notions would appear. Such a theory of quantum mechanics developed in the real space in fact has recently been constructed by the author. The theory started from deeper first principles, namely, from the consideration of the notion of a 4D space-time. So, the notion of fundamental particle, the principles of the motion of a particle and other characteristics have been made clear. The theory, rather a submicroscopic one, is characterized by short-range action that automatically means the introduction of a new kind of carriers, i.e. carriers of the quantum mechanical force. The existence of the carriers called "inertons" (because they carry inert properties of matter) has indeed been verified in a number of experiments.
Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
The physical meaning of Schrödinger’s wave function remains afoundational interpretive question in quantum mechanics. This paperseparates two questions that are often introduced together: what thewave function describes during propagation, and why experimentaloutcomes obey Born statistics. Rather than taking∣Ψ∣2 as the starting definition of Ψ, we begin from theoperational structure of early electron-scattering and transmissionexperiments surrounding the emergence of wave mechanics and Born’s1926 collision theory. Davisson and Kunsman measured angle-dependent collected current,Ramsauer measured energy-dependent electron transmission throughgases, and Dymond later resolved the energy and angular redistributionof electrons after collisions. In each case, the apparatus returnedphysical signals---charge, current, or flux---from which reproducibleoutcome distributions were reconstructed. From this common structure we propose a deliberately limitedinterpretation: for a single nonrelativistic particle, Ψ may beread first as a complex-amplitude representation of thespatial--directional organization of quantum propagation. Thisproposal is anchored not only in the experimental sequence but also inthe mathematics of the wave function. Its Fourier representationresolves propagation into wave-vector components, while theSchrödinger continuity relation defines a conserved density--currentpair; in polar formΨ=Rexp(iS/ℏ),the associated current is proportional toR2∇S. These facts show that Ψ contains both spatial weighting anddirectional phase structure before any additional ontological claim ismade. We do not infer a material wave medium, deterministic particletrajectories, hidden variables, or an alternative dynamics. Nor do wederive the Born rule. Instead, we isolate a separate mapping problem:how does a structured propagation state, through a specific detectorinteraction, become the observed statistics of localized or collectedparticle events? In scattering, any acceptable account must recover the standard fluxand cross-section relations. The contribution of the present paper istherefore interpretive and programmatic: it identifies a constrainedphysical reading of Ψ and states precisely what remains to beexplained.
The study of the behaviour of microscopic systems using Schrodinger's wave equation is a branch of quantum mechanics known as wave mechanics. This approach is inadequate to deal with all problems of interest, but a remarkably wide range of processes can successfully be investigated solely with the theory. The physics of a particle which moves in a static potential is of particular interest. Classically, the energy of such a particle is conserved. The wave function is reminiscent of the classical problem of standing waves on a stretched string with fixed endpoints, with the stationary states corresponding to the normal modes of vibration. Just as there are discrete frequencies of vibration on the string, so there are discrete energy levels. The energy, which is a continuous parameter in classical mechanics, is 'quantized' to certain discrete energy levels.