To the Student

This is a book on the real quantum mechanics. On quantum scales it becomes clear that classical physics is simply wrong. It is quantum mechanics that describes how nature truly behaves; classical physics is just a simplistic approximation of it that can be used for some computations describing macroscopic systems. And not too many of those, either.

Here you will find the same story as physicists tell their own students. The difference is that this book is designed to be much easier to read and understand than comparable texts. Quantum mechanics is inherently mathematical, and this book explains it fully. But the mathematics is only covered to the extent that it provides insight in quantum mechanics. This is not a book for developing your skills in clever mathematical manipulations that have absolutely nothing to do with physical understanding. You can find many other texts like that already, if that is your goal.

The book was primarily written for engineering graduate students who find themselves caught up in nano technology. It is a simple fact that the typical engineering education does not provide anywhere close to the amount of physics you will need to make sense out of the literature of your field. You can start from scratch as an undergraduate in the physics department, or you can read this book.

The first part of this book provides a solid introduction to classical (i.e. nonrelativistic) quantum mechanics. It is intended to explain the ideas both rigorously and clearly. It follows a just-in-time learning approach. The mathematics is fully explained, but not emphasized. The intention is not to practice clever mathematics, but to understand quantum mechanics. The coverage is at the normal calculus and physics level of undergraduate engineering students. If you did well in these courses, you should be able to understand the discussion, assuming that you start reading from the beginning. In particular, you simply cannot skip the short first chapter. There are some hints in the notations section, if you forgot some calculus. If you forgot some physics, just don’t worry too much about it: quantum physics is so much different that even the most basic concepts need to be covered from scratch.

Whatever you do, read all of chapters 2 and 3. That is the very language of quantum mechanics. It will be hard to read the rest of the book if you do not know the language.

Derivations are usually banned to notes at the end of this book, in case you need them for one reason or the other. They correct a considerable number of mistakes that you will find in other books. No doubt they add a few new ones. Let me know and I will correct them quickly; that is the advantage of a web book.

The second part of this book discusses more advanced topics. It starts with numerical methods, since engineering graduate students are typically supported by a research grant, and the quicker you can produce some results, the better. A description of density functional theory is still missing, unfortunately.

The remaining chapters of the second part are intended to provide a crash course on many topics that nano literature would consider elementary physics, but that nobody has ever told you about. Most of it is not really part of what is normally understood to be a quantum mechanics course. Reading, rereading, and understanding it is highly recommended anyway.

The purpose is not just to provide basic literacy in those topics, although that is very important. But the purpose is also explain enough of their fundamentals, in terms that an engineer can understand, so that you can make sense of the literature in those fields if you do need to know more than can be covered here. Consider these chapters gateways into their topic areas.

There is a final chapter in part II on how to interpret quantum mechanics philosophically. Read it if you are interested; it will probably not help you do quantum mechanics any better. But as a matter of basic literacy, it is good to know how truly weird quantum mechanics really is.

The usual Why this book? blah-blah can be found in a note at the back of this book, {N.1} A version history is in note {N.2}.