This open access book develops the world of quantum physics without requiring the onerous math prerequisites of all other texts. Rather than taking just a descriptive approach, or the conventional higher-math approach, this book develops rigorous quantum mechanics beginning at the level of a nonscientist. It is appropriate for advanced high-school students, lifelong learners, citizen scientists, undergraduate students, graduate students, and even current practitioners, engaging a wide group of topics that require no math beyond high-school-level algebra, trigonometry, and geometry. It will also be a source of inspiration for college instructors and high school teachers who are looking for new ways to introduce quantum ideas without overwhelming their students with advanced math. It provides the formal training needed for future work in quantum information science and quantum sensing.
The book begins with quantum reasoning, employing Feynman s methodology to teach many of the mysterious conceptual ideas of quantum mechanics at a level that requires only high-school-level math and no abstraction yet covers advanced ideas, such as delayed choice or interaction-free experiments. It then develops formalism and abstraction while covering undergraduate topics such as spin, harmonic oscillator, angular momentum, interacting spin models, nonrelativistic hydrogen, and particle in a box. The book concludes an advanced treatment of graduate-level topics including time evolution, relativistic hydrogen, Heisenberg spin model, bosons and fermions, Hubbard model, applications to chemistry, quantum simulation, decoherence, second-quantization of light (including gravitational wave detection), and quantum measurements. While the abstraction progresses in sophistication throughout the book, the math never becomes more advanced than complex numbers and linear algebra and is fully self-contained. This volume, the first of two, covers conceptual ideas and quantum-mechanical reasoning, followed by formal developments in single-particle quantum mechanics focused on static properties. It is followed by Volume 2 which covers advanced topics including dynamics, relativity, many-body physics, electron correlations, decoherence, quantization of light, and measurement.
Many of these topics are treated at a level similar to the current state-of-the-art of research in those subjects, going beyond what is typically covered in graduate quantum courses. There is no longer any excuse not to learn about one of the most complex and fascinating developments of human knowledge. Prepare yourself for the second quantum revolution. This book can make everyone into a quantum mechanic. Even you!
