An introduction to wave mechanics

A hydrogen-like atom or ion contains a nucleus and only one electron. 

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It was an exciting place to be for the new, 26-year-old assistant professor of theoretical chemistry, Linus Pauling. He was thrilled to have his first official office (a corner of the X-ray laboratory), his first graduate student (a Texan, J. Holmes Sturdivant, who quickly became a lifelong friend), and his first class to teach ( An Introduction to Wave Mechanics with Applications to Chemistry ). He was... 

An introduction to wave mechanics The wave-nature of electrons... 

This is an introduction to the techniques used for the calculation of electronic excited states of molecules (sometimes called eximers). Specifically, these are methods for obtaining wave functions for the excited states of a molecule from which energies and other molecular properties can be calculated. These calculations are an important tool for the analysis of spectroscopy, reaction mechanisms, and other excited-state phenomena. 

In this section we state the postulates of quantum mechanics in terms of the properties of linear operators. By way of an introduction to quantum theory, the basic principles have already been presented in Chapters 1 and 2. The purpose of that introduction is to provide a rationale for the quantum concepts by showing how the particle-wave duality leads to the postulate of a wave function based on the properties of a wave packet. Although this approach, based in part on historical development, helps to explain why certain quantum concepts were proposed, the basic principles of quantum mechanics cannot be obtained by any process of deduction. They must be stated as postulates to be accepted because the conclusions drawn from them agree with experiment without exception. 

The first two chapters serve as an introduction to quantum theory. It is assumed that the student has already been exposed to elementary quantum mechanics and to the historical events that led to its development in an undergraduate physical chemistry course or in a course on atomic physics. Accordingly, the historical development of quantum theory is not covered. To serve as a rationale for the postulates of quantum theory, Chapter 1 discusses wave motion and wave packets and then relates particle motion to wave motion. In Chapter 2 the time-dependent and time-independent Schrodinger equations are introduced along with a discussion of wave functions for particles in a potential field. Some instructors may wish to omit the first or both of these chapters or to present abbreviated versions. 

You may now wonder what is meant by coherent light. Consider the "Particle in a Box" in Chapter 5, which we used as an introduction to the calculations of Quantum Mechanics. The only energy states which appear for the electron are those for which "standing waves" appear as a function of "1", the length of the "box". To generate coherent light, we set up exactly the same conditions in the form of a resonant cavity. All commercial lasers are based upon this principle, namely that the heart of the laser is this cavity. 

Chemical Reactions in Clusters, E.R. Bernstein Quantum Mechanics in Chemistry, J. Simons and J. Nichols An Introduction to Hydrogen Bonding, G.A. Jeffrey Hydrogen Bonding A Theoretical Perspective, S. Scheiner Fractals in Molecular Biophysics, T.G. Dewey Molecular Orbital Calculations for Biological Systems, A.-M. Sapse An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves. Patterns, and Chaos, I.R. Epstein and J.A. Pojman... 

An introduction to magnetic properties merging classical relationships with quantum mechanical computational recipes constitutes a trait d union between classical and quantum mechanics rather interesting fiom the epistemological point of view. In fact, p(r) and J(r) are subobservables [1], that is, expectation values of corresponding quantum mechanical operators if these expectation values are known as functions in R, a number of molecular electromagnetic properties can be evaluated without the explicit use of electronic wave functions. 

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