- Quantum mechanics1 is the fundamental theoretical infrastructure upon which all understanding of the nature of the physical world is built. This book is an exposition of that theory presented at the level of a junior-year undergraduate physics student. The reader must have attained a level of technical training that includes these essentials:
- A freshman-year survey course in physics. The survey should have included an overview of electricity and magnetism, classical mechanics, and a historical introduction to quantum mechanics2.
- A good grasp of mathematics that includes integral calculus, vector analysis, differential equations, complex numbers, and fourier analysis. The reader should be able to evaluate a determinant and to perform elementary matrix addition and multiplication.
- A first course in classical Newtonian mechanics. The concept of a Hamiltonian and its significance should have been explored.
- In writing this book, I set as my primary task this one: to fuse the mathematical machinery of quantum mechanics3 with the philosophical world view embedded in it.
- That the mathematics appear to grow organically out of the philosophy was my aim in the exposition. My object was to present a consistent physical imagery that tightly parallels the mathematics and thus, with verbal threads, to weave the philosophical tapestry into the mathematical formalism.
- It is incontrovertible that quantum mechanics4 faithfully describes nature’s behavior. To accommodate one’s world view to what is nature’s behavior is the reason for a philosophical tapestry. The tapestry allows us to have a way of perceiving nature as natural.
- In his classic work, Principles of Quantum Mechanics5, P. A. M. Dirac initiated the fusion process. To spotlight the physics within the mathematics, he invented a special notation. Dirac notation embodies the quantum mechanical way of thinking about nature.
- This book is entirely in the language of Dirac notation. My finding has been that even junior-year undergraduates can acquire an impressive facility with Dirac notation when the physical imagery is embedded in the mathematics.
- That imagery must necessarily treat the question "What does quantum mechanics6 tell us about the nature of nature?” This question serves as the underlying theme in the book.
- Primer is meant to be a step in the process that Dirac initiated: to build a quantum intuition; to perceive the quantum universe as self-evident. That the endeavor appears in the format of a primer on the subject is natural: the place to expose the philosophical tapestry is at the first encounter with the formalism.
- The study is pursued by examining what quantum mechanics7 says about the key model physical systems of nature. In the examination are encountered all the practical mathematical techniques useful to a student of the subject.
→ Marvin Chester, Los Angeles, 1987
Advanced Undergraduate level ("Junior-year" in the preface refers to the third of four years' undergraduate study, after Freshman and Sophomore, but before Senior)
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2020
- Mauve: Text by correspondent(s) or other author(s); © the author(s)