Basics of Quantum Mechanics

The study of matter at a molecular and sub-molecular level requires a quantum mechanical framework. In this chapter, we provide an overview of the essential concepts and notation of quantum theory needed to understand the development of relativistic many-electron quantum mechanics. This introductory overview starts from basic axioms with a focus on the nonrelativistic theory. Gauge and Lorentz invariance properties as introduced in the classical theory are then discussed for the basic quantum mechanical equations in the following two chapters. 

The theory of molecular science has to be a custom-made theory of matter on a molecular scale and at energies accessible by thermal motion or photoexcitation. Specifically, we may choose as elementary particles, which compose molecular aggregates, electrons and atomic nuclei to be treated by this theory. It will thus not be necessary to explicitly consider protons or neutrons or even more fundamental particles such as quarks. By choosing electrons and atomic nuclei as the elementary particles of relativistic quantum chemistry, in this book we will elevate the rather general and fundamental quantum mechanical many-electron theory of quantum electrodynamics to a level that allows us to perform actual calculations and simple qualitative considerations of specific systems. Despite these restrictions, a theory for processes at a molecular and sub-molecular scale still has to be quantum mechanical in nature. 

In this section, we shall provide a discussion of elements of quantum mechanics, which have been selected mainly for the purpose of serving the development of relativistic quantum chemistry in later chapters. Unfortunately, in view of the complexity of the subject and the limited space in this book, this conceptual discussion of quantum theory cannot be discussed in satisfactory depth. Also, some aspects will be fully developed only in later chapters. 

In contrast to Newtonian mechanics, we do not have an intuitive access to quantum mechanics. In the case of classical mechanics, Lindsay and Marge-nau [66] coined the term principle of elementary abstraction meaning elementary abstraction from macroscopic observations such as the definition of the velocity as the differential quotient of a length per (infinitesimally) small time interval. Therefore, we proceed to formulate a few non-intuitive postulates 

Relativistic Quantum Chemistry. Markus Reiher and Alexander Wolf 

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One more thing on this topic. There is a lot of tradition in the teaching of science. You simply don t address certain concepts until you get to a particular grade level. This implies that some ideas are much more difficult to understand than others. I strongly believe, however, that anyone can understand, say, the basics of quantum mechanics. Yes, a complete mathematical treatment of the... 

Very often, the famous words of Dirac, i.e., The underl dng physical laws necessary for the mathematical theory of a laige part of physics and the whole of chemistry are thus completely known, are quoted by theorists in physics when they like to underline that chemistry is in principle solved by the basics of quantum mechanics so that some more interesting problems should be solved. Despite this, from 1929 nowadays, quantum physics of atoms and molecules largely turns into quantum chemistry, an interdisciplinary discipline that still struggles with the elucidation of the actual behavior of electrons in nano- and bio-systems. While the total success is... 

Abstract In this chapter we examine some basic concepts of quantum chemistry to give a solid foundation for the other chapters. We do not pretend to review all the basics of quantum mechanics but rather focus on some specific topics that are central in the theoretical description of magnetic phenomena in molecules and extended systems. First, we will shortly review the Slater-Condon rules for the matrix elements between Slater determinants, then we will extensively discuss the generation of spin functions. Perturbation theory and effective Hamiltonians are fundamental tools for understanding and to capture the complex physics of open shell systems in simpler concepts. Therefore, the last three sections of this introductory chapter are dedicated to standard Rayleigh-Schrddinger perturbation theory, quasi-degenerate perturbation theory and the construction of effective Hamiltonians. 

Blokhintsev, D. I. (1961). Basics of Quantum Mechanics, ssllaya shkola, M. 512p. 

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