02-06-2012, 11:02 AM
Quantum Mechanics for Scientists and Engineers
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How to use this book
For teachers
The entire material in this book could be taught in a one-year course. More likely, depending
on the interests and goals of the teacher and students, and the length of time available, only
some of the more advanced topics will be covered in detail. In a two-quarter course sequence
for senior undergraduates and for engineering graduate students at Stanford, the majority of the
material here will be covered, with a few topics omitted and some covered in lesser depth.
The core material (Chapters 1 – 5) on Schrödinger’s equation and on the mathematics behind
quantum mechanics should be taught in any course. Chapter 4 gives a more explicit
introduction to the ideas of linear operators than is found in most texts. Chapter 4 also explains
and introduces Dirac notation, which is used from that point onwards in the book. This
introduction of Dirac notation is earlier than in many older texts, but it saves considerable time
thereafter in describing quantum mechanics. Experience teaching engineering students in
particular, most of whom are quite familiar with linear algebra and matrices from other
applications in engineering, shows that they have no difficulties with this concept.
For students
Necessary background
Students will come to this book with very different backgrounds. You may recently have
studied a lot of physics and mathematics at college level. If so, then you are ready to start. I
suggest you have a quick look at Appendices A and B just to see the notations used in this
book before starting Chapter 2.
Study aids in this book
Lists of concepts introduced
Because there are many concepts that the student needs to understand in quantum mechanics, I
have summarized the most important ones at the end of the Chapters in which they are
introduced. These summaries should help both in following the “plot” of the book, and in
revising the material.
Appendices
The book is as reasonably self-contained as I can make it. In addition to the background
Appendices A and B covering the overall prerequisite mathematics and physics, additional
background material needed later on is introduced in Appendices C and D (vector calculus and
electromagnetism), and one specific detailed derivation is given in Appendix E. Appendix F
summarizes the early history of quantum mechanics, Appendix G collects and summarizes
most of the mathematical formulae that will be needed in the book, including the most useful
ones from elementary algebra, trigonometric functions, and calculus. Appendix H gives the
Greek alphabet (every single letter of it is used somewhere in quantum mechanics), and
Appendix I lists all the relevant fundamental constants.
Problems
There are about 160 problems and assignments, collected at the ends of the earliest possible
Sections rather than at the ends of the Chapters.
Memorization list
Quantum mechanics, like many aspects of physics, is not primarily about learning large
numbers of formulae, but rather understanding the key concepts clearly and deeply. It will,
however, save a lot of time (including in exams!) to learn a few basic formulae by heart, and
certainly if you also understand these well, you should have a good command of the subject.
At the very end of the book, there is a list of formulae worth memorizing in each Chapter of
the book. None of these formulae is particularly complicated – the most complicated ones are
the Schrödinger wave equation in its two forms. Many of the formulae are simply short
definitions of key mathematical concepts. If you learn these formulae chapter by chapter as
you work through the book, there are not very many formulae to learn at any one time.