Chaos in Classical and Quantum Mechanics (Interdisciplinary Applied Mathematics) (v. 1) [Hardcover]

Martin C. Gutzwiller (Author)

Book Description

ISBN-10: 0387971734 | ISBN-13: 978-0387971735 | Publication Date: October 23, 1990 | Edition: 1st

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

Product Details

• Hardcover: 452 pages
• Publisher: Springer; 1st edition (October 23, 1990)
• Language: English
• ISBN-10: 0387971734
• ISBN-13: 978-0387971735
• Product Dimensions: 9.6 x 6.4 x 1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #1,583,516 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

5.0 out of 5 stars Chatty and fun, but not to be used as the basis for anything but a reading course, April 14, 2007

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Scott C. Locklin "Selectos nisi das mihi libe... (Berkeley CA) - See all my reviews
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This review is from: Chaos in Classical and Quantum Mechanics (Interdisciplinary Applied Mathematics) (v. 1) (Hardcover)

There are all kinds of physics books. There are books for didactics; nobody actually uses, say, Jackson's book on Classical Electrodynamics for anything but didactics. You can tell the books that are useful for teaching in a classroom by the presence of extensive problem sets. This book has none. So, with this, let me dispose of the notion that you should be able to teach a 'quantum chaos' course based on this book. There are also books which explain in great technical detail all about a given small subject area; Fritz Haake's book on 'Quantum Signatures of Chaos' is a good example of this (though it's really about Random Matrix theory, which is but one quantum signature of chaos; a whole book on just one small area of this subject -covered in a few pages in Gutzwiller's book). Then there are books which are reviews of a subject. Gutzwiller wrote a book which is a review of a subject. It's a very good one.

One could actually go through this, read it, know about the existence of many things, and read up on them as is appropriate for one's research. That is how I used the book. Gutzwiller writes very well, and communicates his enthusiasm for the subject matter. The bibliography is extensive, and you could indeed learn all about anything you needed to by going through the bibliographic references for the details. An actual review which takes you from knowing about Hamilton Jacobi theory and the WKB approximation and covering all the material he presented in every detail needed to understand the whole mess .... I doubt as any such book exists. It would be an encyclopedia. If you simply want to understand the Gutzwiller trace formula starting at that level, there are books which do it reasonably well (Cvitanovic's is a great effort in that direction). This is not such a book; this is a review. A review of a very important body of work. That is this book's purpose, and it serves it admirably well.

As for why Gutzwiller is important; if you think the correspondence principle is interesting, the Gutzwiller trace formula is the main useful way we know of thinking about it in detail. Most physicists think about the area where quantum mechanics becomes classical as a sort of intellectual blur. This is a mistake. This is arguably a much more interesting place to think about than, say, what happened in the first 10^-35 seconds of the big bang. For example, one can actually do experiments in the semiclassical regime. Experiments which only involve optics. There's gold in them there hills, and nobody is looking there. Mesoscopic physics as applied to device physics may eventually force people to think about these issues in detail, but I somehow doubt the device guys are going to reinvent quantum mechanics. Gutzwiller thought about these issues in the 1960s while working on practical problems for IBM. These are the fundamental mysteries, folks: if you're an ambitious young physicist who wants to make a real contribution to science; leave the noodle theory alone, and look into this stuff. Following the herd will get you a nice career, but immortality belongs to the one who plays Einstein or Poincare to Gutzwiller's Minkowski.

5 of 6 people found the following review helpful:

5.0 out of 5 stars Absolute Reference for Quantum Chaos, December 25, 2000

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"masuzen" (Muenchen, Germany) - See all my reviews

This review is from: Chaos in Classical and Quantum Mechanics (Interdisciplinary Applied Mathematics) (v. 1) (Hardcover)

Organization and presentation of the ideas of modern chaos theory for classical and quantum world without deeper mathematical proofs in perfect fashion meets in this book. Historical, mathematical and physical origins of the chaos and semiclassical quantization problems have appeared as an introductory. Topics covered with great care, If you like to have a good foundation in this field, this book is absolute must. It served as a guide where to go in quantum chaos. Read it word by word and consult many references in nature of classical, statistical and quantum mechanical, differential geometrical and applied mathematics. Excellent book.

4 of 5 people found the following review helpful:

5.0 out of 5 stars Gutzwiller's Chaos in Classical and Quantum Mechanics, April 29, 2000

By 

Osher Doctorow, Ph.D. - See all my reviews

This review is from: Chaos in Classical and Quantum Mechanics (Interdisciplinary Applied Mathematics) (v. 1) (Hardcover)

The first thing a non-specialist should do is to hire a reputable consultant or tutor to translate this book into approximately ordinary English, but it would be a bad mistake to miss this book because it is full of remarkable ideas that apply to almost every field. To show you how translation would work, it turns out that doughtnuts (torus, plural tori in math) are key to classical and quantum chaos. You might ask: why doughtnuts, instead of, say, balls (beachballs, tennis balls, microscopic balls, etc.)? Well, let's consider a person's head as a ball. You can comb a person's hair flat on his head, but not without a part or irregularity (eddy) somewhere - see page 33 of the book, which says this is slightly different words. On a doughnut, however, you can comb hair flat without any irregularities. The hair with the directions in which they point are called vectors in mathematics, and all together they form a vector field. Chaos occurs when these doughtnuts get disturbed, say by raising the energy (perturbations). Gutzwiller of IBM New York pioneered the study of the relationship between classical and quantum chaos, but anybody who has read IBM books or manuals know that they usually require heavy translation. If you absolutely can't find a math or physics consultant or tutor, go through Gutzwiller's book page by page until you find something like this which you can understand, and keep reading the comprehensible paragraphs.