Quantum Mechanics Homework

Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane waves. This explanation was proposed by the author in 1963 when the author had been studying Quantum Mechanics. Self-action in a system of elementary particles, charged with elementary charges, is discussed in detail. This self-action is not taken in account in Quantum Mechanics, because otherwise experimental data (including data on atomic spectra) could not be theoretically explained. In Quantum Mechanics sometimes there is an electrostatic field without any electrostatic energy stored in it, and electrostatic negative energy with no charge and no electrostatic field, like in a positronium. Criteria for low-dimensional quantum movements are derived, quantum and classical rotations of modern objects are regarded. Simplified theory of polarons and bipolarins is proposed, and simple explanation of coexistence of zero angular momentum and non-zero magnetic moment in many-electron system is discussed.

Quantum mechanics (QM) is latently present in the life of electrical engineers already, since the hardware of todays information technology - from electrical data processing, through interconversion of electronic and optical information, to data storage and visualization - works on QM principles. New developments in micro- and opto-electronics and the advent of quantum information processing will soon make the active understanding of QM unavoidable for engineers, too. Unfortunately, the principles of QM can only be formulated mathematically, so even introductory books on the subject are mostly rather abstract. This book, written mainly for BSc students, tries to help the reader by showing "QM in action", demonstrating its surprising effects directly in applications, like lighting technology, lasers, photo- and solar cells, flash memories and quantum bits. While the axioms and basic concepts of quantum mechanics are introduced without compromises, the math is kept at a level which is required from electrical engineers anyhow. Computational work is spared by the use of Applets which also visualize the results. Among the host of other didactic features are learning objectives, chapter summaries, self-testing questions, and problems with solutions, while two appendices summarize the knowledge in classical physics and mathematics which is needed for this book.

This book presents a complete review of the theory of nonlinear quantum mechanics and which differs totally from the original discipline of quantum mechanics as well as the studies the nature of microscopic particles under action of the nonlinear interactions in the systems; which give numerous new and interesting properties and rules of motions of the particles, such as wave-corpuscle duality and localization, and which discusses the applications of theory as relates to condensed matter, polymers, and biological systems. It is intended for researchers, teachers, graduate students and upper-level undergraduate students. The so-called discipline of nonlinear quantum mechanics (NLQM) is, in reality, only a theory for studying the properties and motion of microscopic particles (MIPs) in nonlinear physical systems. It was so named in relation to the concept of quantum mechanics established by Bohr, Heisenberg, Schrodinger and numerous others. The latter deals only with the properties and motion of microscopic particles in linear systems without nonlinear interactionh and will, here-in-after, referred to as linear quantum mechanics (LQM). The following topics are covered in 6 chapters i

To combine the formulas of GR and QM to calculate something, the same answer is always yielded: infinity, still unsolved. The issue of space-time curvature, Problem of quantization, Universe is non-local or local, particles are zero dimensional or what?, Background of space-time and matter, superposition of states and so on are few of unsolved problems of QM and Relativity. We have observed a relation between reciprocity and quantum statistics. Reciprocity may be a bridge between QM and Relativity which is a great unsolved problem. We have defined Reciprocal Symmetry and we have applied it to find an invariant under addition. This invariant quantity is either an upper bound of a set of quantities or a lower bound of the reciprocals of this set. The set bounded above together with this invariant quantity corresponds to Einstein’s postulate. we find that discreteness is directly related Einstein’s postulate or Lorentz transformation. We have seen that Reciprocals and reciprocal symmetry relate Einstein’s postulate and Lorentz transformation to discreteness, wave motion and Fermi-Dirac statistics. Reciprocal symmetry, therefore, relates quantum mechanics (QM) to relativity.

"As Towfic Shomar argues, if we are looking for quantum description that gives very accurate predictions about superconducting phenomena we can make do with the "phenomenological" equations of Ginzburg-Landau model, These equations are phenomenological in two senses: First, they are not derived by constructing a model to which a Hamiltonian is assigned, but rather are justified by an ad hoc combination of considerations from thermodynamics, electro-magnetism and quantum mechanics itself. Second, the model does not give us any representation of the causal mechanisms that might be responsible for superconductivity." Nancy Cartwright, from her book: "The Dappled World", CUP, Cambridge 1999, pp 193-4.

Based on the law of energy conservation, the author shows that, the steady state electronic motion around a given nucleus in a non-circular orbit, depicts a rest mass variation, though the overall relativistic energy remains constant. This is, in no way, conflicting with the usual quantum mechanical approach. Quite on the contrary it provides one with the possibility of bridging the Special Theory of Relativity and Quantum Mechanics, to finally achieve a natural symbiosis between these two disciplines, and furthermore, elucidating the “quantum mechanical weirdness”, simply based on the mere law of relativistic energy conservation. The author developed his theory, originally, vis-a-vis gravitational bodies in motion with regards to each other; hence, it is comforting to have both the atomic scale and the celestial scale described on just the same conceptual basis. The approach leads to the de Broglie relationship, and superluminal speeds, yet excluding any exchange of energy, making the basis of quantum mechanics.

Rarely, the authors of quantum mechanics books have discussed Dirac – Jordan transformation theory in abstract and pure form . Mostly, in the topics of mathematical tools, quantum mechanics assimilates in a manner with matrices theory that and its operability and ability differentiates as a pure theory is difficult. The subject of this study is that to show the ability of this theory in different discussions and particular differences of its solution methods with other theories. Principally, applied mathematics in Dirac – Jordan transformation theory is particular and differs with the mathematics present in theorems and relations of wave and matrices theories . Encountering with wave and matrices theories maybe implies, at least, applied mathematics in these theories gives certain relation between them, but there is not the case of Dirac – Jordan transformation theory. Quantum state of a particle in a given time, in Schrodinger’s wave theory, was defined by wave function . Probabilistic interpretation of this wave function requires that its square could be integrated, and this leads to study Hilbert, H space.

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