Mathematical Physical Chemistry

This book introduces basic concepts of mathematical physics to chemists. Many textbooks and monographs of mathematical physics may appear daunting to them. Unlike other, related books, however, this one contains a practical selection of material, particularly for graduate and undergraduate students majoring in chemistry. The book first describes quantum mechanics and electromagnetism, with the relation between the two being emphasized. Although quantum mechanics covers a broad field in modern physics, the author focuses on a hydrogen(like) atom and a harmonic oscillator with regard to the operator method. This approach helps chemists understand the basic concepts of quantum mechanics aided by their intuitive understanding without abstract argument, as chemists tend to think of natural phenomena and other factors intuitively rather than only logically. The study of light propagation, reflection, and transmission in dielectric media is of fundamental importance. This book explains these processes on the basis of Maxwell equations. The latter half of the volume deals with mathematical physics in terms of vectors and their transformation in a vector space. Finally, as an example of chemical applications, quantum chemical treatment of methane is introduced, including a basic but essential explanation of Green functions and group theory. Methodology developed by the author will also prove to be useful to physicists.

Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. Numerous examples and problems interspersed throughout the presentations Each extensive chapter contains a preview, objectives, and summary Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics

By the time chemistry students are ready to study physical chemistry, they’ve completed mathematics courses through calculus. But a strong background in mathematics doesn’t necessarily equate to knowledge of how to apply that mathematics to solving physicochemical problems. In addition, in-depth understanding of modern concepts in physical chemistry requires knowledge of mathematical concepts and techniques beyond introductory calculus, such as differential equations, Fourier series, and Fourier transforms. This results in many physical chemistry instructors spending valuable lecture time teaching mathematics rather than chemistry. Barrante presents both basic and advanced mathematical techniques in the context of how they apply to physical chemistry. Many problems at the end of each chapter test students’ mathematical knowledge. Designed and priced to accompany traditional core textbooks in physical chemistry, Applied Mathematics for Physical Chemistry provides students with the tools essential for answering questions in thermodynamics, atomic/molecular structure, spectroscopy, and statistical mechanics.

This text provides students with concise reviews of mathematical topics that are used throughout physical chemistry. By reading these reviews before the mathematics is applied to physical chemical problems, a student will be able to spend less time worrying about the math and more time learning the physical chemistry.

The third edition of this book has been updated so that both advanced physics and advanced chemistry can be overviewed from a modern mathematical perspective in a single integrated book. Nowadays key research arears in physics and chemistry such as materials science, molecular science, and device physics are drawing closer and closer together and becoming more and more mathematical. Hence, while retaining the basic feature, the contents are targeted at graduate and undergraduate students majoring in not only chemistry but also physics and engineering. The book covers topics ranging from classical physics (e.g., electromagnetism and analytical mechanics) to quantum science. The latter topic includes an introduction to the quantum theory of fields as well as standard quantum mechanics and quantum chemistry. Tangible examples help readers to understand abstract concepts about the topics covered. Several major revisions have been made and they contain: (a) constitution of the Dirac equation; (b) quantization of the fields; (c) interaction between the quantum fields; (d) basic formalism related to the extended vector spaces and the transformation properties of the Dirac equation; (e) advanced topics of Lie algebra. The new edition thus supplies chemists, physicists, and engineers with fundamental knowledge and calculation methodology of mathematical physics.

Mathematical Physics in Theoretical Chemistry deals with important topics in theoretical and computational chemistry. Topics covered include density functional theory, computational methods in biological chemistry, and Hartree-Fock methods. As the second volume in the Developments in Physical & Theoretical Chemistry series, this volume further highlights the major advances and developments in research, also serving as a basis for advanced study. With a multidisciplinary and encompassing structure guided by a highly experienced editor, the series is designed to enable researchers in both academia and industry stay abreast of developments in physical and theoretical chemistry. Brings together the most important aspects and recent advances in theoretical and computational chemistry Covers computational methods for small molecules, density-functional methods, and computational chemistry on personal and quantum computers Presents cutting-edge developments in theoretical and computational chemistry that are applicable to graduate students and research professionals in chemistry, physics, materials science and biochemistry

Introduction to problems of molecular structure and motion covers calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics. Answers to problems. 1966 edition.