Quantum Mechanics: From Basic Principles to Numerical Methods and Applications

ISBN-13: 9783642077678 / Angielski / Miękka / 2010 / 560 str.

Louis Marchildon

Opis

Whoever begins writing a book on quantum mechanics is struck by the breadth of the subject. In its applications first: atomic and molecular p- sics, nuclear physics, optics, solid state physics, theory of gases and liquids, elementary particles theory, almost all fields of contemporary physics are based on quantum mechanics. In its formulation, also, which borrows from many subfields of mathematics and reaches philosophical reflection as much as modern technology. The writing therefore implies, at the outset, making choices. I first chose to write a book for those who strive to understand qu- tum mechanics. These are physics students, of course, but also students and investigators in theoretical chemistry, biophysics and engineering physics w- hing to comprehend more deeply the computational methods they use. I have thus tried to clarify delicate points rather than leave them aside. Conceptual problems are treated in more detail than in most general textbooks. But understanding also involves the capability to perform concrete calculations. This motivates the development of numerical methods which, most of the time, are the only ones that yield quantitative results. I chose also to present quantum mechanics as a self-contained theory. The exposition largely develops around the central notion of state space.

Recenzje

From the reviews:

"This is an interesting a valuable book for someone who wants to obtain a solid understanding of the fundamental aspects of quantum mechanics, an appreciation of some aspects of the numerical solution of practical applications, and an introduction or better to a very broad spectrum of topics."-Chemistry in Asutralia Magazine of the Royal Astralian Chemical Institute

"This is an expository book on Quantum Mechanics. The exposition largely develops around the central notion of state space. ... Although the exposition is largely self contained, numerous references are given to books and research papers. This is a very useful book for undergraduate and graduate students who study Quantum Mechanics." (T. C. Mohan, Zentralblatt MATH, Vol. 1033 (8), 2004)

"There are some excellent and classic texts on quantum mechanics (QM) ... . The present monograph represents an attempt to rewrite and rearrange the outlook and topics ... . Overall the book offers a rich mix of topics and is highly readable. The exercises at the end of each chapter represent a reasonable collection for the students to test their comprehension and assimilation of the subject matter. It is a welcome addition to the large number of books on QM." (Mayer Humi, Mathematical Reviews, 2003 m)

"His 'exposition largely develops round the central notion of state space'. ... This could be a useful book for an advanced graduate course or theoretical specialists and a useful reference for others ... ." (Alastair Rae, Times Higher Education supplement, May, 2003)

"I like this book, and I'll probably use it as a reference and resource for my Honours year quantum mechanics course. ... One of the strengths of this book is the thorough treatment of atomic theory ... ." (Craig Savage, The Physicist, Vol. 39 (6), 2002)

"This is an interesting and valuable book for someone who wants to obtain a solid understanding of the fundamental aspects of quantum mechanics ... . For those higher year undergraduate and graduate students of physical and theoretical chemistry who want to teach themselves quantum mechanics, this book might provide a better route than other standard texts." (Michael Collins, Chemistry in Australia, January/February, 2003)

Spis treści

1 A Crisis in Classical Physics.- 2 Finite-Dimensional Vector Spaces.- 3 Finite-Dimensional State Spaces.- 4 Spin and Magnetic Moment.- 5 Particle in One Dimension.- 6 The Interpretation of Quantum Mechanics.- 7 Particle in Three Dimensions.- 8 Numerical Solution.- 9 The Central-Field Model.- 10 Stationary Perturbations.- 11 Stationary Scattering States.- 12 The Density Operator.- 13 Symmetry of the Hamiltonian.- 14 Rotations and Angular Momentum.- 15 Dirac’s Relativistic Equation.- 16 The Path Integral.- 17 Atomic Orbitals.- 18 Atomic Terms and Multiplets.- 19 Semiclassical Radiation Theory.- 20 Molecules.- 21 Long-Distance Correlations and Measurement.- Answers to Selected Exercises.- References.

Blurb

This advanced text develops first the underlying concepts of quantum mechanics, thus starting with state spaces of finite dimension followed by the representation of coordinates with their principal formal elements, and their applications such as the harmonic oscillator, magnetic momentum, the hydrogen atom, stationary perturbations etc. This fresh and original text on quantum mechanics focuses on: the development of numerical methods for obtaining specific results; the presentation of group theory and the systematic use of operators; the introduction of the functional integral and its applications in approximation; the discussion of distant correlations and experimental measurements. Numerous exercises with hints and solutions, examples and applications, and a guide to key references help the student to work with the text.