Advanced Visual Quantum Mechanics

Abstract

Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. But despite its use of modern visualization techniques, it is a conventional textbook of (theoretical) quantum mechanics. You can read it without a computer, and you can learn quantum mechanics from it without ever using the accompanying CD-ROM. But, the animations will greatly enhance your understanding of quantum mechanics. They will help you to get the intuitive feeling for quantum processes that is so hard to obtain from the mathematical formulas alone. A first book with the title Visual Quantum Mechanics (“Book One”) appeared in the year 2000. The CD-ROM for Book One earned the European Academic Software Award (EASA 2000) for outstanding innovation in its field. The topics covered by Book One mainly concerned quantum mechanics in one and two space dimensions. Advanced Visual Quantum Mechanics (“Book Two”) sets out to present three-dimensional systems, the hydrogen atom, particles with spin, and relativistic particles. It also contains a basic course of quantum information theory, introducing topics like quantum teleportation, the EPR paradox, and quantum computers. Together, the two volumes constitute a fairly complete course on quantum mechanics that puts an emphasis on ideas and concepts and satisfies some modest requirements of mathematical rigor. Nevertheless, Book Two is fairly self-contained. References to Book One are kept to a minimum so that anyone with a basic training in quantum mechanics should be able to read Book Two independently of Book One. Appendix A includes a short synopsis of quantum mechanics as far as it was presented in Book One. Computer visualizations are particularly rewarding in quantum mechanics because they allow us to depict objects and events that cannot be seen by other means. However, one has to be aware of the fact that the animations depict the mathematical objects describing reality, not reality itself. Usually, one needs some explanation and interpretation to understand the visualizations. The visualization method used here makes extensive use of color. It displays all essential information about the quantum state in an intuitive way. Watching the numerous animations will thus create an intuitive feeling for the behavior of quantum systems—something that is hardly achieved just by solving the Schr¨odinger equation mathematically. I would even say that the movies allow us to see the whole subject in a new way. In any case, the “visual approach” had a great influence on the selection of topics as well as on the style and the level of the presentation. For example, Visual Quantum Mechanics puts an emphasis on quantum dynamics, because a movie adds a natural time-dimension to an illustration. Whereas other textbooks stop when the eigenfunctions of the Hamiltonian are obtained, this book will go on to discuss dynamical effects. It depends on the situation, but also on the personality of the student or of the teacher, how the movies are used. In some cases, the movies are certainly useful to stimulate the student’s interest in some phenomenon. The animation thus serves to motivate the development of the theory. In other cases, it is, perhaps, more appropriate to show a movie confirming the theory by an example. Personally, I present the movies by video projection as a supplement to an introductory course on quantum mechanics. I talk about the movies in a rather informal way, and soon the students start asking interesting questions that lead to fruitful discussions and deeper explanations. Often, the movies motivate students to study related topics on their own initiative.