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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 approx-imation 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 there 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. non-relativistic) quantum mechanics. It is intended to explain the ideas both rig-orously and clearly. It follows a “just-in-time” learning approach. The mathe-matics 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 sec-tion, 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

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basic concepts need to be covered from scratch.

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 funda-mentals, 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 on how to interpret quantum mechanics philosoph-ically. 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}.

Acknowledgments

This book is for a large part based on my reading of the excellent book by Griffiths, [21]. It now contains essentially all material in that book in one way or the other. (But you may need to look in the notes for some of it.) This book also evolved to include a lot of additional material that I thought would be appropriate for a physically-literate engineer. There are chapters on relativity, numerical methods, thermodynamics, solid mechanics, electromagnetism, and nuclei.

Somewhat to my surprise, I find that my coverage actually tends to be closer to Yariv’s book, [43]. I still think Griffiths is more readable for an engineer, though Yariv has some very good items that Griffiths does not.

The idea of using the Lagrangian for the derivations of relativistic mechanics is from A. Kompanayets, theoretical physics, an excellent book.

PREFACE xli The nanomaterials lectures of colleague Anter El-Azab that I audited in-spired me to add a bit on simple quantum confinement to the first system studied, the particle in the box. That does add a bit to a section that I wanted to keep as simple as possible, but then I figure it also adds a sense that this is really relevant stuff for future engineers. I also added a discussion of the effects of confinement on the density of states to the section on the free-electron gas.

I thank Swapnil Jain for pointing out that the initial subsection on quantum confinement in the pipe was definitely unclear and is hopefully better now.

I thank Johann Joss for pointing out a mistake in the formula for the aver-aged energy of two-state systems.

The discussions on two-state systems are mainly based on Feynman’s notes, [18, chapters 8-11]. Since it is hard to determine the precise statements being made, much of that has been augmented by data from web sources, mainly those referenced.

The discussion of the Onsager theorem comes from Desloge, [9], an emeritus professor of physics at the Florida State University.

The section on conservation laws and symmetries is almost completely based on Feynman, [18] and [16].

Harald Kirsch reported various problems in the sections on conservation laws and on position eigenfunctions.

The note on the derivation of the selection rules is from [21] and lecture notes from a University of Tennessee quantum course taught by Marianne Breinig.

The subsection on conservation laws and selection rules was inspired by Ellis, [11].

The many-worlds discussion is based on Everett’s exposition, [13]. It is brilliant but quite impenetrable.

The section on the Born-Oppenheimer approximation comes from Wikipe-dia, [[21]], with modifications including the inclusion of spin.

The section on the Hartree-Fock method is mainly based on Szabo and Ostlund [40], a well-written book, with some Parr and Yang [29] thrown in.

The section on solids is mainly based on Sproull, [36], a good source for practical knowledge about application of the concepts. It is surprisingly up to date, considering it was written half a century ago. Various items, however, come from Kittel [24]. The discussion of ionic solids really comes straight from hyperphysics [[7]]. I prefer hyperphysics’ example of NaCl, instead of Sproull’s equivalent discussion of KCl. My colleague Steve Van Sciver helped me get some handle on what to say about helium and Bose-Einstein condensation.

The thermodynamics section started from Griffiths’ discussion, [21], which follows Yariv’s, [43]. However, it expanded greatly during writing. It now comes mostly from Baierlein [4], with some help from Feynman, [15], and some of the books I use in undergraduate thermo.

The derivation of the classical energy of a spinning particle in a magnetic field is from Yariv, [43].

The initial inspiration for the chapter on nuclear physics was the Nobel Prize acceptance lecture of Goeppert Mayer [[10]]. This is an excellent introduction to nuclear physics for a non-specialist audience. It is freely available on the web. As the chapter expanded, the main references became the popular book by Krane [26]. That book is particularly recommended if you want an understandable description of how the experimental evidence led physicists to formulate the theoretical models for nuclei. Other primary references were [30] and [34]. The Handbook of Physics, Hyperphysics, and various other web sources were also helpful. Much of the experimental data are from NUBASE 2003, an official database of nuclei, [3]. Updates after 2003 are not included. Data on magnetic moments derive mostly from a 2001 preprint by Stone; see [39]. Nu-Dat 2 [[13]]

provided the the excited energy levels and additional reference data to validate various data in [39].

The discussion of the Born series follows [21].

The brief description of quantum field theory and the quantization of the electromagnetic field is mostly from Wikipedia, [[21]], with a bit of fill-in from Yariv [43], Feynman [15], Kittel [24], and citizendium [[3]]. The example on field operators is an exercise from Srednicki [37], whose solution was posted online by a TA of Joe Polchinski from UCSB.

Acknowledgements for specific items are not listed here if a citation is given in the text, or if, as far as I know, the argument is standard theory. This is a text book, not a research paper or historical note. But if a reference is appropriate somewhere, let me know.

Grammatical and spelling errors have been pointed out by Ernesto Bosque, Eric Eros, Samuel Rustan, Mark Vanderlaan, and Ramaswami Sastry Vedam. I will try to keep changing “therefor” into “therefore,” but they do keep sneaking in.

Thank you all.