Semiclassical way to quantum mechanics

This paper attempts to summarise the basics of a radical new field in particle physics: quantum mechanics. It includes an in-depth explanation of 4 basic concepts of quantum mechanics, which are Quantum Field Theory, Deriving the Theory of Addition of Velocities or Distances, Deriving how E=mc2 was modified for massless and stationary particles and The Heisenberg Uncertainty Principle.

Rethinking Quantum Mechanics./Journal of Applied Physics (IOSR-JAP)., 2018

Annotation: The possibility has been shown to obtain the key results of quantum mechanics with no resort to specific postulates based on the thermodynamics of stationary processes. A derivation of the Planck radiation law has been offered to proceed from the assumption the wave is a true quantum of radiation. It has been found that the average energy of such a quantum is numerically equal to the Planck constant. The law of spectral series formation has been obtained without the use of quantum numbers. The photo-effect equation has been supplemented taking into consideration the photoelectric yield. A hypothesis-free derivation of the Schrödinger stationary equation has been given along with its modification as a kinematic first-order equation. The possibility has been shown to consider quantum mechanics as a branch of classical physics studying wave processes.

By the end of the nineteenth century theoretical physicists thought that soon they could pack up their bags and go home. They had developed a powerful mathematical theory, classical mechanics, which seemed to described just about all that they observed, with the exception of a few sticking points. In particular the classical world was ruled by Newtonian physics where matter (atoms) interacted with a radiation field (light) as described by Maxwell's equations. However as it turned out these sticking points were not smoothed over at all but rather were glimpses of the microscopic (and relativistic) world which was soon to be experientially discovered. As has been stated countless times, by the end of the first decade of the twentieth century quantum mechanics and relatively had appeared and would soon cause classical mechanics, with its absolute notions of space, time and determinacy to be viewed as an approximation. Historically the first notion of quantized energy came in 1900 with Planck's hypothesis that the energy contained in radiation could only be exchanged in discrete lumps, known as " quanta " , with matter. This in turn implies that the energy, E, of radiation is proportional to its frequency, ν, E = hν (1.1) with h a constant, Planck's constant. This allowed him to derive his famous formula for black body spectra which was in excellent agreement with experiment. From our perspective this is essentially a thermodynamic issue and the derivation is therefore out of the main theme of this course. The derivation of such a formula from first principles was one of the sticking points mentioned above. While Planck's derivation is undoubtedly the first appearance of quantum ideas it was not at all clear at the time that this was a fundamental change, or that there was some underlying classical process which caused the discreteness, or that it was even correct. However there were further experiments which did deeply challenge the continuity of the world and whose resolution relies heavy on Planck's notion of quanta.

183 philosophical implications of quantum mechanics and develop a new way of thinking about nature on the nanometer-length scale. This was undoubtedly one of the most signiicant shifts in the history of science. The key new concepts developed in quantum mechanics include the quantiza-tion of energy, a probabilistic description of particle motion, wave–particle duality, and indeterminacy. These ideas appear foreign to us because they are inconsistent with our experience of the macroscopic world. Nonetheless, we have accepted their validity because they provide the most comprehensive account of the behavior of matter and radiation and because the agreement between theory and the results of all experiments conducted to date has been impressively accurate. Energy quantization arises for all systems whose motions are connned by a potential well. The one-dimensional particle-in-a-box model shows why quantiza-tion only becomes apparent on the atomic scale. Because the energy level spacing is inversely proportional to the mass and to the square of the length of the box, quantum effects become too small to be observed for systems that contain more than a few hundred atoms. Wave–particle duality accounts for the probabilistic nature of quantum mechanics and for indeterminacy. Once we accept that particles can behave as waves, we can form analogies with classical electromagnetic wave theory to describe the motion of particles. For example, the probability of locating the particle at a particular location is the square of the amplitude of its wave function. Zero-point energy is a consequence of the Heisenberg indeterminacy relation; all particles bound in potential wells have nite energy even at the absolute zero of temperature. Particle-in-a-box models illustrate a number of important features of quantum mechanics. The energy-level structure depends on the nature of the potential, E n n 2 , for the particle in a one-dimensional box, so the separation between energy levels increases as n increases. The probability density distribution is different from that for the analogous classical system. The most probable location for the particle-in-a-box model in its ground state is the center of the box, rather than uniformly over the box as predicted by classical mechanics. Normalization ensures that the probability of nding the particle at some position in the box, summed over all possible positions, adds up to 1. Finally, for large values of n, the probability distribution looks much more classical, in accordance with the correspondence principle. Different kinds of energy level patterns arise from different potential energy functions, for example the hydrogen atom (See Section 5.1) and the harmonic oscil-lator (See Section 20.3). These concepts and principles are completely general; they can be applied to explain the behavior of any system of interest. In the next two chapters, we use quantum mechanics to explain atomic and molecular structure, respectively. It is important to have a rm grasp of these principles because they are the basis for our comprehensive discussion of chemical bonding in Chapter 6.

Physics Essays, 2012

Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between 'canonically conjugated' coordinate and momentum operators leads to a wrong version of quantum mechanics. In this connection the Feynman integral formalism is also discussed. In this formalism the measure is not well-defined and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one; it is rather a mnemonic rule to generate perturbation series from an undefined zero order term. The origin of time is analyzed in detail by the example of atomic collisions. It is shown that the time-dependent Schrödinger equation for the closed three-body (two nuclei + electron) system has no physical meaning since in the high impact energy limit it transforms into an equation with two independent time-like variables; the time appears in the stationary Schrödinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system. Following the Einstein-Rosen-Podolsky experiment and Bell's inequality the wave function is interpreted as an actual field of information in the elementary form. The relation between physics and mathematics is also discussed.