Preface to the First Edition
The contents of this book are based upon manuscripts prepared for both undergraduate courses of Kyoto Institute of Technology by the author entitled “Polymer
Nanomaterials Engineering” and “Photonics Physical Chemistry” and a master’s
course lecture of Kyoto Institute of Technology by the author entitled “Solid-State
Polymers Engineering.”
This book is intended for graduate and undergraduate students, especially those
who major in chemistry and, at the same time, wish to study mathematical physics.
Readers are supposed to have a basic knowledge of analysis and linear algebra.
However, they are not supposed to be familiar with the theory of analytic functions
(i.e., complex analysis), even though it is desirable to have relevant knowledge
about it.
At the beginning, mathematical physics looks daunting to chemists, as used to be
the case with myself as a chemist. The book introduces the basic concepts of
mathematical physics to chemists. Unlike other books related to mathematical
physics, this book makes a reasonable selection of material so that students majoring
in chemistry can readily understand the contents in spontaneity. In particular, we
stress the importance of practical and intuitive methodology. We also expect engineers and physicists to benefit from reading this book.
In Part I and Part II, the book describes quantum mechanics and electromagnetism. Relevance between the two is well considered. Although quantum mechanics
covers the broad field of modern physics, in Part I we focus on a harmonic oscillator
and a hydrogen (like) atom. This is because we can study and deal with many of
fundamental concepts of quantum mechanics within these restricted topics. Moreover, knowledge acquired from the study of the topics can readily be extended to
practical investigation of, e.g., electronic states and vibration (or vibronic) states of
molecular systems. We describe these topics by both analytic method (that uses
differential equations) and operator approach (using matrix calculations). We believe
that the basic concepts of quantum mechanics can be best understood by contrasting
the analytical and algebraic approaches. For this reason, we give matrix representations of physical quantities whenever possible. Examples include energy
ix
The contents of this book are based upon manuscripts prepared for both undergraduate courses of Kyoto Institute of Technology by the author entitled “Polymer
Nanomaterials Engineering” and “Photonics Physical Chemistry” and a master’s
course lecture of Kyoto Institute of Technology by the author entitled “Solid-State
Polymers Engineering.”
This book is intended for graduate and undergraduate students, especially those
who major in chemistry and, at the same time, wish to study mathematical physics.
Readers are supposed to have a basic knowledge of analysis and linear algebra.
However, they are not supposed to be familiar with the theory of analytic functions
(i.e., complex analysis), even though it is desirable to have relevant knowledge
about it.
At the beginning, mathematical physics looks daunting to chemists, as used to be
the case with myself as a chemist. The book introduces the basic concepts of
mathematical physics to chemists. Unlike other books related to mathematical
physics, this book makes a reasonable selection of material so that students majoring
in chemistry can readily understand the contents in spontaneity. In particular, we
stress the importance of practical and intuitive methodology. We also expect engineers and physicists to benefit from reading this book.
In Part I and Part II, the book describes quantum mechanics and electromagnetism. Relevance between the two is well considered. Although quantum mechanics
covers the broad field of modern physics, in Part I we focus on a harmonic oscillator
and a hydrogen (like) atom. This is because we can study and deal with many of
fundamental concepts of quantum mechanics within these restricted topics. Moreover, knowledge acquired from the study of the topics can readily be extended to
practical investigation of, e.g., electronic states and vibration (or vibronic) states of
molecular systems. We describe these topics by both analytic method (that uses
differential equations) and operator approach (using matrix calculations). We believe
that the basic concepts of quantum mechanics can be best understood by contrasting
the analytical and algebraic approaches. For this reason, we give matrix representations of physical quantities whenever possible. Examples include energy
ix