When compared to classical mechanics (CM), quantum mechanics (QM) clearly appears as a difficult topic to the beginner. However, some knowledge of the basics of QM is a real need also for learners with predominant interest in experimental chemistry. Indeed, QM is the physical theory explaining most fundamental aspects of Chemistry, such as the periodic table of the elements and the chemical bond now called covalent, found by 19th century chemists and for a long time recognized as incompatible with the physical theories of the time (CM and classical electromagnetism). Going beyond the historical point of view, many peculiar aspects of QM and its very language permeate all modern chemistry so that a trustworthy understanding is required to deal with the matter in a sensible way.
When compared to classical mechanics (CM), quantum mechanics (QM) clearly appears as a difficult topic to the beginner. However, some knowledge of the basics of QM is a real need also for learners with predominant interest in experimental chemistry. Indeed, QM is the physical theory explaining most fundamental aspects of Chemistry, such as the periodic table of the elements and the chemical bond now called covalent, found by 19th century chemists and for a long time recognized as incompatible with the physical theories of the time (CM and classical electromagnetism). Going beyond the historical point of view, many peculiar aspects of QM and its very language permeate all modern chemistry so that a trustworthy understanding is required to deal with the matter in a sensible way.
This introductory chapter provides an overview of quantum mechanics, which is a subject of central importance in chemistry, and is by nature a mathematical theory. The chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of constituent molecules. However, at the microscopic level, atoms, molecules, and their constituent particles do not obey the familiar laws of mechanics that pertain to the everyday macroscopic world. For example, the existence of molecular line spectra indicates that molecules can be found only at certain well-defined energies, unlike objects at our own scale whose energy appears to be continuously variable. This book aims to explain the fundamentals of quantum mechanics from the point of view of chemistry; describe the areas of chemistry where quantum mechanics is most important; and show how quantum mechanics is applied to chemical problems.
Quantum mechanics is the key to modern physics and chemistry, yet it is notoriously difficult to understand. This book is designed to overcome that obstacle. Clear and concise, it provides an easily readable introduction intended for science undergraduates with no previous knowledge of quantum theory, leading them through to the advanced topics usually encountered at the final year level.Although the subject matter is standard, novel techniques have been employed that considerably simplify the technical presentation. The authors use their extensive experience of teaching and popularizing science to explain the many difficult, abstract points of the subject in easily comprehensible language. Helpful examples and thorough sets of exercises are also given to enable students to master the subject.
Quantum Mechanics 1 starts from the basis that quantum mechanics is of central importance in chemistry. To understand matter and its chemical transformation it is necessary to take a microscopic view connecting experimental observation to the properties of constituent molecules. However, at this microscopic level, atoms and sub-atomic particles do not obey the classical laws of mechanics that pertain to the everyday macroscopic world. They obey the laws of quantum mechanics. This text explains the fundamentals of quantum mechanics from the point of view of chemistry; describes areas of chemistry where quantum mechanics is most important; and shows how quantum mechanics is applied to chemical problems. To this end, the book is divided into two parts: the first deals with the foundations of quantum mechanics (concentrating on exactly soluble problems and the reduction of complicated problems to simple foundations) and the second is a tool kit for applying quantum mechanics to chemical problems (thus concentrating on approximate methods).
The objective of this chapter is to go over a few of the basic concepts of quantum mechanics in preparation for a discussion of spectroscopy, which is in many ways the business end of quantum mechanics, at least for chemical scientists. We will also need a few quantum mechanical ideas from time to time in our study of thermodynamics and of kinetics. Why should we learn quantum mechanics at all? Atoms and molecules are small, and their constituent parts, electrons, protons and neutrons, are even smaller. Early in the twentieth century, we learned that small things don't obey the laws of classical mechanics. A different kind of mechanics, quantum mechanics, is required to understand chemistry on a fundamental level. In fact, we need different mechanical theories to treat extremes of both size and speed. Figure 2.1 summarizes the situation. There isn't a sharp cut-off between the various sectors of this diagram. Also note that some of the theories are more general than others. We could in principle use quantum mechanics or general relativity to predict the trajectories of tennis balls, but it just isn't worth the effort, given that classical mechanics works perfectly well in this range of masses and speeds. On the other hand, classical mechanics doesn't give very good results for things that are either extremely large, or small, or fast. Like it or not, to discuss phenomena on an atomic scale, we need quantum mechanics. Ordinary (non-relativistic) quantum mechanics is generally adequate, although electrons in heavy atoms sometimes reach relativistic speeds (approaching the speed of light, c ), requiring relativistic quantum mechanics.
Quantum Mechanics 2 opens by stating that the chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of the constituent molecules. Atoms and sub-atomic particles do not obey the classical laws of mechanics but conform rather to the laws of quantum mechanics. Quantum mechanics is thus of central importance in chemistry. In order to understand the behaviour of molecules and their constituent particles it is necessary to have a thorough grounding in the principles and applications of quantum mechanics. This text provides a toolkit for applying quantum mechanics to chemical problems, introducing more advanced approaches using approximate methods. It describes areas of chemistry where quantum mechanics is important, and shows how quantum mechanics can be applied to chemical problems.
Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.