This chapter discusses important peculiarities of quantum systems by using the submicroscopic concept. It focuses on the derivation of the Schrodinger equation, the physical interpretation of the wave ψ-function and looks at the interior of other well-established notions of quantum mechanics. The chapter considers the basic notions of quantum mechanics, such as tunneling and Heisenberg's uncertainty principle. It discusses inertons emitted by the particle at its motion. The inerton cloud spreads out to the distance Λ from the particle in the transverse directions. The inerton cloud is able to interact with obstacles and transfers the appropriate information to the particle. Since the inerton cloud carries the particle's mass, the fluid element in question can be specified with both mass and volume. The chapter considers the motion of inertons emitted by the moving particle. The mother-particle, which creates inertons, moves in ajerky manner caused by its continuous periodic stopping, and its inerton cloud behaves similarly.
This chapter discusses important peculiarities of quantum systems by using the submicroscopic concept. It focuses on the derivation of the Schrodinger equation, the physical interpretation of the wave ψ-function and looks at the interior of other well-established notions of quantum mechanics. The chapter considers the basic notions of quantum mechanics, such as tunneling and Heisenberg's uncertainty principle. It discusses inertons emitted by the particle at its motion. The inerton cloud spreads out to the distance Λ from the particle in the transverse directions. The inerton cloud is able to interact with obstacles and transfers the appropriate information to the particle. Since the inerton cloud carries the particle's mass, the fluid element in question can be specified with both mass and volume. The chapter considers the motion of inertons emitted by the moving particle. The mother-particle, which creates inertons, moves in ajerky manner caused by its continuous periodic stopping, and its inerton cloud behaves similarly.
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10^{-28} cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons". The further study has disclosed that inertons are a substructure of the matter waves which are described by the orthodox wave ψ-function formalism. The concept has allowed resolving the spin problem. The theory, or more exactly, the existence of inertons, has been verified experimentally: in rarefied gases, inerton clouds of atoms' electrons interact with a strong laser pulse; in a solid, atom's inertons induce an additional harmonic potential that contributes to the interatomic interaction (metal specimens and the KIO_3*HIO_3 crystal).
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.
Abstract The second chapter introduces the notion of wave functions and their equation of motion proposed by Erwin Schrödinger. The interpretation and normalization of the wave function are discussed, leading to the continuity equation. The chapter also introduces basic mathematical operations that can be carried out for wave functions and operators, describing e.g., how to calculate scalar products and commutators, as well as expectation values and variances of observables. With these tools at hand, Heisenberg’s uncertainty principle is re-examined, focusing on the example of a Gaussian wave packet, which is studied both in position space and momentum space. We also discuss the time evolution of general states and of the exemplary wave packet. Finally, we will see how classical physics is recovered as a limiting case of the quantum-mechanical description
This chapter discusses the central concepts and equations of quantum theory which demonstrates how particles spread through space like waves and are described mathematically by a wavefunction. It examines how the wavefunction is interpreted and introduces the uncertainty principle, which is one of the most profound departures of quantum mechanics from classical mechanics. It also highlights the dynamical properties of a system that are contained in the wavefunction and are obtained by solving the Schrödinger equation. The chapter reconciles the facts that atoms and molecules can possess only certain energies, that waves exhibit the properties of particles, and that particles exhibit the properties of waves. It reviews the classical concept that have been accommodated by the development of quantum mechanics, in which equations are set up to treat a particle as spread through space like a wave.
Introduction In this chapter we discuss the basic physical concepts and equations related to the behavior of particles in the nanoworld. We introduce the Schrödinger wave equation for particles and determine the ways to calculate observable physical quantities. We find that, in wave mechanics, the motion of a particle confined to a finite volume is always characterized by discrete values of the energy and standing-wave-like wavefunctions, i.e., such a motion is quantized. While motion in an infinite space (i.e., free motion) is not quantized and is described by propagating waves, the energy of the particle is characterized by a continuous range of values. Keeping in mind the diverse variants of nanostructures, by using wave mechanics we analyze some particular examples, which highlight important quantum properties of particles. Many of the examples analyzed can serve as the simplest models of nanostructures and will be exploited in following chapters to understand the fundamentals of processes in nanoelectronics. The Schrödinger wave equation From the previous chapter, we conclude that nanosize physical systems are quantum-mechanical systems, inasmuch as their sizes are comparable to typical de Broglie wavelengths of the particles composing these systems. In dealing with quantum-mechanical systems, one aims at determining the wavefunction of a single particle or of the whole system. As we will demonstrate in the subsequent discussion, knowledge of the wavefunction in quantum mechanics is sufficient to describe completely a particle or even a system of particles.
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wave function is subatomic particle moving randomly. Therefore, the characteristics of quantum mechanics have a dual nature, one of them is the deterministic nature carried on from classical physics, and the other is the probabilistic nature coined by particle's random motion. Based on this model, almost all of open questions in quantum mechanics can be explained consistently, which include the particle-wave duality, the principle of quantum superposition, the interference pattern of double-slit experiments, and the boundary between the classical world and the quantum world. The current quantum mechanics is a mixture of matrix mechanics and wave mechanics, which are sharply conflicting in principle. Matrix mechanics treats quantum particles as classical particles with fixed relation between the particle's position and its momentum. The matrix mechanics, in fact, belongs to the old quantum theory. Both Born's non-commutative relation and Heisenberg uncertainty relation originate from matrix mechanics. However, in wave mechanics, there is no any fixed relation between the particle's position and its momentum, and the particle's position and its momentum belong to immeasurable physical quantities. Therefore, there is no need for non-commutative relation and uncertainty relation in wave mechanics.