Search results for ""author marian apostol""

Quantum Mechanics is a fundamental scientific discipline. At the same time, it is viewed as being very difficult. This book attempts to present the Theory of Quanta as a scientific discipline which has emerged naturally from experiment, making use of general concepts of the Classical Mechanics and enlarging their nature and applicability. According to the historical development, the first natural way of introducing the quantum-mechanical concepts is the matricial theory, followed by the very useful approach of the undulatory theory. The core of the Theory of Quanta is the quasi-classical theory, described at large in the book. The book does not circumvent the so-called philosophical problems of the Quantum Mechanics. 1) Ch. 1, Beginnings, includes all the experimental, preliminary indications of the necessity of a new theory. The usual textbooks say little about this aspect. In particular, Double Slit and Particle and Waves sections are completely new. 2) Ch. 2, Classical Mechanics, is seldom included in the usual textbooks. In addition, it is formulated here on the basis of the Hamilton-Jacobi equation, though rarely used, it is the direct way of passing from the Classical Mechanics to the Theory of Quanta. The Lenz vector in the central field is emphasized, the only way to deduce the hydrogen atom by using the Matricial Theory, a fundamental result. 3) Ch. 3, Quantum Mechanics, is the exposition of the matricial method. This is the core of the Theory of Quanta, which exhibits the basic ingredients. The Matricial theory is not included today in textbooks, which prefer the Wave Mechanics (Schrodinger equation). It is shown here the direct way to Schrodinger equation from the Matricial Theory. This chapter is written from the little-known book by Born and Jordan, Matricial Mechanics (cited there). 4) Chs. 4 to 8 are standard, technical subjects, with many novelties: Coulomb degeneracy, adiabatic hypothesis, second quantization and many-body theories (the latter is never included in textbooks). 5) Ch. 9, Quasi-Classical Quantum Mechanics, is completely new. In particular, the Tunneling, the Chemical Reactivity, Adiabatic Transitions, Reflexion above Barrier (with many applications, to ionization, for instance) are described in detail. Also, in this chapter the "philosophical" problems of the Theory of Quanta are discussed. The Quasi-Classical Mechanics is the most interesting subject in the Theory of Quanta. 6) Ch. 10, Scattering, includes a completely new formulation. Usually, the scattering theory is presented in a very fastidious way. There is a much simpler way, leading directly to results, which is present in this chapter. The clue to the scattering theory is the solution of the Helmholtz equation, usually overlooked. 7) Finally, Ch. 11 includes the much discussed problem of Measurement. The most advanced result in this direction belongs to Pauli (in his book on Quantum Mechanics). The result is still unsatisfactory. A more direct description of the measurement is given here, based on the very quantum-mechanical principles. The results are perfectly convincing, and, of course, new. 8) It is indeed hard to believe that something new can be said about the Theory of Quanta. A great impediment in understanding the Quantum Mechanics is because there are too many books published on the subject. The subject was distorted in all imaginable ways, every author trying to be original. I hope that I have succeeded to be as close as possible to the original meaning of the subject, without being too original.

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The Theory of Quanta has a large area of applicability. Any motion, at the fundamental level, is quantum-mechanical, or includes quantum-mechanical motion. Quantum Mechanics encompasses motion forms from atoms, to atomic nuclei, molecules, chemical binding, electric and magnetic fields, electromagnetic radiation, and transport phenomena. The book includes such quantum-mechanical theories, both in their standard form and original versions, with emphasis on their physical contents. 1) Ch. 1, The Atom, besides standard subjects, presents a new, original formulation of the Thomas-Fermi theory, which allows the possibility to arrive at new results like giant dipole oscillations in heavy atoms, atom ionization and chemical bonding. 2) Ch. 2, Molecules, puts emphasis on molecular spectra, including a semi-classical treatment of rotation spectra. The Jahn-Teller effect, with its various implications in many other areas, is discussed in detail. 3) Ch.3, The Atomic Nucleus, includes an original treatment of the nuclear dynamics, based on the mean-field idea. In particular, the Weizsacker mass formula is derived, nuclear instabilities are discussed and the statistical approach is presented. 4) Chs. 5-7 include an original presentation of the Electric and Magnetic Fields effects on atoms. The tunneling, both in static and oscillating electric fields, is presented, with application to atomic ionization, as well as the proton emission and the effect of high-intensity electric fields on alpha decay. The new subject of scattering of charges by laser pulses is presented in detail. 5) An interesting, new subject of transitions under change of parameters, including the dynamical Berry phase is given in Ch. 8, Change of Parameters. 6) Ch. 9, Stimulated Magnetic Resonance, presents a new phenomenon of magnetic resonance, generated by stimulated emission. 7) Ch. 10, Quantized Conductance, presents a new, original way of deriving the quanta of conductance in ballistic transport, or in magnetic field. 8) Ch. 11, Coherence, gives an extended account of the coherent interaction of the electromagnetic radiation with polarizable matter, with implication on the superradiance transition and possible new phenomena occurring in water. 9) Ch. 12, Chemical Bonding, is a description of the original theory of chemical bonding, based on the linearized Thomas-Fermi theory, with its basic application to formation of the metallic clusters. 10) Ch. 13, Quantum Theory of Radiation, is an exposition of the Dirac theory of radiation, and the interaction of the radiation with matter, following Fermi's famous article, a subject seldom presented in usual textbooks, in spite of its fundamental relevance. 11) The book ends with a thorough discussion of the place of the Quantum Mechanics in the realm of the Physical Science disciplines, emphasizing the fundamentally new, and very fruitful, quantum-mechanical vision.

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