In applied physics and in engineering intuitive understanding is a boost for creativity and almost a necessity for efficient product improvement. The existence of soliton solutions to the quantum equations in the presence of self-interactions allows us to draw an intuitive picture of quantum mechanics. The purpose of this work is to compile a collection of models, some of which are simple, some are obvious, some have already appeared in papers and even in textbooks, and some are new. However this is the first time they are presented (to our knowledge) in a common place attempting to provide an intuitive physical description for one of the basic particles in nature: the electron. The soliton model applied to the electrons can be extended to the electromagnetic field providing an unambiguous description for the photon. In so doing a clear image of quantum mechanics emerges, including quantum optics, QED and field quantization. To our belief this description is of highly pedagogical value. We start with a traditional description of the old quantum mechanics, first quantization and second quantization. We describe an intuitive description of first and second quantization based on the concept of solitons, pioneered by the double solution of de Broglie in 1927. Many aspects of first and second quantization are clarified and visualized intuitively, including the so called vacuum fluctuations.
In applied physics and in engineering intuitive understanding is a boost for creativity and almost a necessity for efficient product improvement. The existence of soliton solutions to the quantum equations in the presence of self-interactions allows us to draw an intuitive picture of quantum mechanics. The purpose of this work is to compile a collection of models, some of which are simple, some are obvious, some have already appeared in papers and even in textbooks, and some are new. However this is the first time they are presented (to our knowledge) in a common place attempting to provide an intuitive physical description for one of the basic particles in nature: the electron. The soliton model applied to the electrons can be extended to the electromagnetic field providing an unambiguous description for the photon. In so doing a clear image of quantum mechanics emerges, including quantum optics, QED and field quantization. To our belief this description is of highly pedagogical value. We start with a traditional description of the old quantum mechanics, first quantization and second quantization. We describe an intuitive description of first and second quantization based on the concept of solitons, pioneered by the double solution of de Broglie in 1927. Many aspects of first and second quantization are clarified and visualized intuitively, including the so called vacuum fluctuations.
Chapter 4 deals with Quantum Mechanical (QM) phenomena. The first section describes the first attempts at quantization of energy, momentum, angular momentum, etc. We start with Plank's solution to the black-body problem, introducing the concept of photons: discrete packets of electromagnetic energy. We show how Plank's description of black-body radiation is perfectly fit by the cosmic microwave radiation, providing the strongest evidence for the Big-Bang at the origin of the Universe. We then describe Bohr's solution to the paradoxical stability of atoms, introducing quantization of angular momentum (or action) and correctly predicting the energy levels of the hydrogen atom. We show how Einstein used Plank's idea to explain the photo-electric effect (an effect exploited in CCD cameras and solar cells) and how he used Bohr's understanding of energy levels in atoms to provide an intuitive explanation of Plank's law. Einstein insight opened the way to the field of spectroscopy and the development of the laser. In the second section, following the lead of Dirac, we show that QM is equivalent to Linear Algebra in the space of complex functions (which describe the state of the system). We show that Schrödinger's equation is a natural consequence of that description, once the relation between energy and frequency established by Plank (for photons) and de Broglie (for particles) is taken into account. In the context of the chiral ammonia molecule we discuss the queerness of QM which describes physical systems as superposition of states (such as left and right chirality state of a molecule, dead and alive cat). We show that this queerness is nonetheless supported by experiments and is behind much of our technology: masers and lasers, atomic clocks, semiconductors (diodes, transistors, etc.). In the following section we introduce the representation of operators in QM (the equivalent of matrices in linear algebra): momentum, position, energy, etc. which correspond to measurements on the system. We show that the non-commutability of some operators (common with matrix operations) leads to Heisenberg uncertainty principle: the position and momentum of a particle cannot be determined with absolute precision. We discuss the solution of Schrödinger's equation for free particles demonstrating their equivalence with EM phenomena: particles undergo refraction and diffraction, exemplifying the particle/wave duality inherent to QM systems. We discuss QM tunneling and its use in the Scanning Tunneling Microscope. In the following section we study Dirac's equation: the successful attempt by Dirac to unify QM with Einstein's relativity, with the resulting prediction of anti-particles and spin. We then solve for the energy levels of electrons in the hydrogen atom (from Schrödinger's equation) and show that the existence of spin profoundly affects the behavior of electrons in an atom: they cannot share the same energy level, a rule known as Pauli's exclusion principle. Pauli's principle is central to the understanding of the chemical properties of atoms and fully explains Mendeleev's periodic table of the elements. In the next section we discuss along with two exactly soluble systems (diatomic rotational and vibrational levels), various approximations used to study systems (e.g. molecules) for which there are no analytical solutions. In particular, we introduce Pauling's variational approach, Hückel molecular orbital theory and time independent perturbation theory. We apply those approaches to determine the energy levels in alkenes, in multi-electron atoms and in systems under constant electric or magnetic field (such as in Magnetic Resonance Imaging). In the last section we discuss time dependent perturbation theory. We use it to establish the rules allowing for transitions between energy levels and revisit Einstein description of absorption/emission phenomena.
Schrödinger’s wave mechanics, developed in a series of papers published one century ago, offered an exceptionally intuitive route into the new atomic physics. The later axiomatic formulation of quantum mechanics brought indispensable mathematical precision, but it can also conceal the physical images that guided the original discovery. We revisit the optical–mechanical analogy behind Schrödinger’s construction and use it as a visual guide to stationary states, superposition, field modes, and gauge interactions. The analogies are deliberately heuristic and their limitations are stated: a quantum wavefunction is not, in general, a classical wave in ordinary space, and discrete classical modes do not by themselves imply quantized energy. Nevertheless, the wave viewpoint makes it possible to see the operator language of first and second quantization as the compact algebraic expression of an underlying mode structure. The purpose of this article is therefore not to replace the modern formalism, but to recover the physical intuition that makes that formalism intelligible.
Abstract Fundamental concepts about the structure of matter have been analyzed based on cause-and-effect relations leading to the postulates of quantum mechanics. The interpretation of the characteristics of a vacuum as properties of a universal carrier medium in terms of fluid mechanics has made it possible to select consistent models of the basic objects of condensed matter. The development of concepts of the structure of the photon and electron has been supplemented by descriptions of the processes of their production and transformation. The nature of electric charges and the picture of their interaction through volumetric interference fields have been discussed. The details of the structure of the atom, the sizes of electron orbits, and the internal characteristics of some elementary particles have been clarified. The physical nature of the quantization of matter at different dimensional and energy levels has been determined. The proposed solutions to problems of a quantum can be useful for the range of physicists dealing with problems that are fundamentally unsolvable in traditional terms.
Preface. Introduction to the Conference. A Quantum of Light Shed on a Classical Problem C.K. Whitney. A Classical Photon Model R.J. Beil. Stationary Vacuum-Polarization 'P Fields': the Missing Element in Electromagnetism and Quantum Mechanics M.H. MacGregor. Electrons and Photons as Soliton-Waves G. Hunter. Topological Solitons in Non-Linear Electrodynamics G. Kalbermann. A Particle or a Photon in a Field T.W. Marshall, E. Santos. Could the Photon be Superfluous? M. Sachs. Fluctuation-Dissipation Quantum Electrodynamics G.F. Efremov, et al. Einstein-de-Broglie-Proca Theory of Light and Simultaneous Existence of Transverse and Longitudinal Photons S. Roy, M. Roy. Origin, Observation and Consequences of the B(3) Field M.W. Evans. Opto-Magnetic Effects in Non-Absorbing Media: Problems of Measurement and Interpretation S. Jeffers, et al. Generalized Equations of Electrodynamics of Continuous Media V.M. Dubovik, et al. Maxwellian Analysis of Reflection and Refraction R.D. Prosser, et al. Solutions of Maxwell Equations for a Hollow Curved Wave Conductor N. Bashkov, A. Tchernomorov. Maxwell's Equations Directly from the Dynamics of Point Particles G.N. Ord. Obtaining the Schrodinger and Dirac Equations from the Einstein/KAC Model of Brownian Motion by Projection G.N. Ord. Derivation of the Schrodinger Equation T.B. Andrews. An Appraisal of Stochastic Interpretations of Quantum Mechanics M. Baublitz, Jr. Compatible Statistical Interpretation of Quantum Beats M. Bozic. Stochastic Non-Markov Model of Quantum Mechanical Behaviour S.R. Vatsya. A Fundamental Force as the Deterministic Explanation of Quantum Mechanics B.J. Dalton. A Geometric Approach to the Quantum Mechanics of the Broglie and Vigier W.R. Wood, G. Papini. Stable Orbits as Limit Cycles S. Bergia. The Correspondence Principle: Periodic Orbits from Quantum Mechanics D. Provost. Neutron Interferometric Experiments on Quantum Mechanics G. Badurek. Enigmatic Neutrons V.K. Ignatovich. Experiments to Test the Reality of De Broglie Waves J.R. Croca. Preselected Quantum Optical Correlations M. Pavicic. Apparent Contradiction in EPR Correlations L.C. Ryff. The Wave- particle Duality E. Bitsakis. Quantum Mechanical Tunneling in a Causal Interpretation M. Clarkson. Quantum Uncertainty, Wave-particle Duality and Fundamental Symmetries P. Rowlands. On the Contradiction between Quantum Mechanics and Relativity: a Superluminal Quantum Morse Telegraph A. Garuccio. Incompatibility between Einstein's Relativity and Lorentz's Equations P. Marmet. On Self-Interaction and (Non-)Perturbative Quantum GRT H.-H. von Borzeszkowski. Classical Physics Foundations for Quantum Physics L. Motz, D.W. Kraft. Inertial Transformations: A Review F. Selleri. The Lorentz Invariance Revisited M. Surdin. A New Type of Massive Spin-One Boson: And Its Relation with Maxwell Equations D.V. Ahluwalia. Implications of Extended Models of the Electron for Particle Theory and Cosmology E.J. Sternglass. The Takabayasi Moving Frame, from the A Potential to the Z Boson R. Boudet. The Nature of the Cosmological Redshift M. Moles. A Quantum Digital Theory of Light N.V. Pope. Toward a Comprehensible Physical Theory: Gravity and Quantum Mechanics H. Yilmaz. Hidden Background Field and Quantum Non-Locality R. Ramanathan. Einstein-Podolsky-Rosen Correlations within Bell Region R. Horodecki. Electromagnetic Gauge as Integration Condi
Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics
I. Brief History.When I first learned of this conference, and saw the wide range of interests represented by the participants, I was certain that finally a common definition of that most intriguing concept-the soliton-would emerge.And I was anxious that this definition be broad enough to encompass solitons in both their classical and quantum versions.For recent work had convinced me that the general technique known as Bethe's ansatz for solving diverse one-dimensional quantum problems in fact was nothing more nor less than the quantum soliton.However, from conversations with conference participants, I discovered that many were not aware of this accumulated work on exactly soluble quantum systems.I even gained the impression that some feel quantum mechanics to be much harder than classical mechanics-an unnecessary complication.My own feeling, on the other hand, is that in many cases quantum mechanics clarifies matters.It forces one to immediately face problems that would eventually have to be faced in the corresponding classical case, problems such as the counting of states, to determine how important solitons really are.Anyway, the history of the quantum soliton is all to the greater glory of the soliton concept.And quite a respectable history it is.I would date the beginning at 1931 with a paper of H. Bethe [1] on magnetism; that is a total span of 45 years.Quantum mechanics itself has not been around all that much longer!It now seems my hopes for a consensus on a definition of the soliton were premature, and things are still fermenting.Nevertheless, here is my contribution to the conference in the form of a brief history for general interest, and a more original work on the quantization of the Toda lattice.Perhaps next time there will be some consolidation, and we can then decide just how particular and how general a concept is the soliton.1.We begin this historical account with the classic paper of H. Bethe [1], which introduced first the many-body wave function crucial