The Bell That Rings Light: A Primer in Quantum Mechanics And Chemical Bonding (Mathematics Across the Curriculum) [Paperback]

Dorothy Wallace (Author), Joseph J. Belbruno (Author)

Book Description

Publication Date: September 7, 2006 | ISBN-10: 9812567062 | ISBN-13: 978-9812567062

This book is an introduction to quantum mechanics and mathematics that leads to the solution of the Schrodinger equation. It can be read and understood by undergraduates without sacrificing the mathematical details necessary for a complete solution giving the shapes of molecular orbitals seen in every chemistry text. Readers are introduced to many mathematical topics new to the undergraduate curriculum, such as basic representation theory, Schur's lemma, and the Legendre polynomials.

Editorial Reviews

Review

"It probably serves best as supplementary material, either for mathematics students to see how some seemingly abstract mathematics has been applied to physical systems or for science students to appreciate the logical system that underpins familiar physical models."Choice

Product Details

• Paperback: 137 pages
• Publisher: World Scientific Pub Co Inc (September 7, 2006)
• Language: English
• ISBN-10: 9812567062
• ISBN-13: 978-9812567062
• Product Dimensions: 9 x 6.9 x 0.4 inches
• Shipping Weight: 6.4 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,162,778 in Books (See Top 100 in Books)

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4 of 4 people found the following review helpful:

5.0 out of 5 stars Understanding the hydrogen atom via the Schrodinger Equation, January 9, 2009

By 

Mead C. Whorton Jr. (Bastrop, LA United States) - See all my reviews
(REAL NAME)   

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This review is from: The Bell That Rings Light: A Primer in Quantum Mechanics And Chemical Bonding (Mathematics Across the Curriculum) (Paperback)

Dorothy Wallace has written a wonderful primer of quantum mechanics and the mathematics underlying the Schrodinger equation which allows one to grasp the basic structure of the hydrogen atom. Dr. Wallace pulls no punches in the mathematics involved so the reader will need a basic knowledge of calculus and at least know what a differential equation is to follow her well reasoned book. Before one tackles this text, I would recommend reading Thirty Years that Shook Physics by George Gamow and Quantum Mechanics for Chemists by David O. Hayward. Armed with historical knowledge from Gamow's book and a basic understanding of quantum mechanics (Chapters 1-6) from Hayward's book, the reader will easily follow most of the concepts in this superb book by Wallace. Wallace initially sketches concepts of Rutherford, Bohr, and Balmer and follows this with short chapters on some early experiments and early quantum mechanics of the hydrogen atom. She then introduces the Schrodinger equation, classical waves, and particles in a box. Next, the reader is introduced in several chapters to Fourier coefficients, the Laplace operator, quantum numbers, the group SO(3,R), spherical harmonics, and Laguerre polynomials. After two short chapters on bonding and valence shell electron repulsion; she presents two beautifully written chapters, replete with vibrant, color computer graphics, on the shape of an orbital and molecular orbital theory. These two chapters are the very nexus of the book and were very enlightening to me. The book concludes with chapters on valence bond theory, other kinds of bonding, and a case study: Dye Molecules. In my opinion, these last three chapters will be of great interest to chemistry students. I attempted to read Griffiths' Introduction to Quantum Mechanics prior to reading this book but the mathematical formalism was a little too difficult for me. After reading Gamow, Hayward, and this volume; I would suggest that the reader delve into the philosphical battles about quantum mechanics picture of reality which raged during the 1920s. Einstein and Bohr were at the heart of this intellectual conflict. The struggle for the soul of science involving the dispute over quantum mechanics is beautifully portrayed in Einstein Defiant by Bolles and Uncertainty by Lindley. Dr. Wallace has written a lucid explanation of how Schrodinger's equation allows us to grasp the structure of the hydrogen atom. Her primer presents the material in a mathematically sophisticated manner but not at a level which will leave the reader hopelessly lost in the abstract mathematical formalism of quantum mechanics. THE BELL THAT RINGS LIGHT will reveal the beauty of the hydrogen atom as portrayed by the Schrodinger equation to any reader who is willing to take pen and paper in hand and work through the mathematics. I do wish that she would post a few simple problems on her website with worked out solutions. In conclusion; a primer which will, in time, become a classic for beginners.

2 of 2 people found the following review helpful:

5.0 out of 5 stars A remarkable book worthy of becoming a classic, October 16, 2010

By 

AC (Michigan) - See all my reviews

This review is from: The Bell That Rings Light: A Primer in Quantum Mechanics And Chemical Bonding (Mathematics Across the Curriculum) (Paperback)

There are some topics which are taken on by all manner of those who deem themselves qualified to teach it to others. For those topics which tend to be considered difficult, let alone seemingly taught in much the same manner regardless of author, one can at times find it futile to continue seeking a potentially alternate method by which to learn such a topic.

But then every now and then, one might stumble upon a highly welcome surprise: an exception, let alone a gem. This book is such an exception, and gem.

To the original reviewer's comments, I would simply like to add the following: an excerpt from the author's Preface -

"... And because of that little book, for the last twenty years I have made it my hobby to piece together the story of the hydrogen atom, how it grew from a simple little sun-plus-planet into the set of equations that Schrodinger gave, and how the solution to those equations answers questions posed by Bohr himself.
This little book is a gift to myself. It is the book I wish I had found next to those two others when I went to the library, so that I could have reached, with my still limited knowledge of physics and mathematics, the place where the other books began. This book is for you, too, especially if you are taking a physics or chemistry course now. In it, you will find some glue to help patch up your picture of the universe, especially the very small things in it."


I, as well, wish a book like this had existed years ago. On the bright side, it now exists - and would be a wonderful resource to have available to students across the country, by ensuring that a copy is available in (at least) public libraries.

The approach used by this author in having carefully dissected the subject, & skillfully woven step-by-step aspects together in a clear & cohesive manner, is exceptional, & most importantly, effective. The tone is almost conversational, which adds to the appeal, & frankly, in my opinion, is a non-trivial contributor to the presentation's effectiveness (it would also seem to play a role in softening potentially intimidating aspects of the subject for many readers/students). In a way, the writing combines elements which take on the feel of having a dinner conversation with the author, with logically interspersed let-me-show-you -like explanatory specifics included when appropriate, & that might involve a drawing or diagram at times, & at other times, a step-by-step clarification of relevant mathematical equations.

This book is a highly welcome creation, & a truly exceptional accomplishment & educational resource.

I felt compelled to write a review after seeing that only one review existed. This book deserves serious & voluminous praise, & I am grateful to the author for her having been motivated to & tenaciously pursued lucid explanatory approaches to the many facets of quantum mechanics & chemical bonding during the twenty year prelude which led to this book.

Very, Very Nicely Done - and Thank You...