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Quantum Mechanics in Simple Matrix Form
This elementary text introduces basic quantum mechanics to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part of the quantum language and apply it to problems.
Emphasizing the matrices representing physical quantities, it describes states simply by mean values of physical quantities or by probabilities for possible values. This approach requires using the algebra of matrices and complex numbers together with probabilities and mean values, a technique introduced at the outset and used repeatedly. Students discover the essential simplicity of quantum mechanics by focusing on basics and working only with key elements of the mathematical structure--an original point of view that offers a refreshing alternative for students new to quantum mechanics.
Emphasizing the matrices representing physical quantities, it describes states simply by mean values of physical quantities or by probabilities for possible values. This approach requires using the algebra of matrices and complex numbers together with probabilities and mean values, a technique introduced at the outset and used repeatedly. Students discover the essential simplicity of quantum mechanics by focusing on basics and working only with key elements of the mathematical structure--an original point of view that offers a refreshing alternative for students new to quantum mechanics.
288 pages, Paperback
First published December 20, 2005
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Displaying 1 - 3 of 3 reviews
May 25, 2012
A hard book with some eye watering derivations. HOWEVER the author does seek to shed some light on the "strange equation" that started it all. The last few chapters show how Lie groups are basic to the representation of physical quantities if these quantities are going to be invariant through changes in position, time, orientation and velocity. I think this is what is covered in advanced books, but it is explained here in an elementary way.
January 21, 2018
Plus:
The math is *in theory* relatively basic. There's no calculus or differential equations or eigenvectors or any of the revolting mathematics that goes beyond that. This is entirely matrix algebra, and how it can be used to understand quantum mechanics. In particular, the first few chapters provide an excellent review of basic math (complex numbers, matrix operations, etc.) for people who aren't familiar or who have forgotten certain topics. Naturally, problem sets are included at the end of each chapter.
Minus:
For one, the book assumes an engaged and motivated audience. There's no good explanation of the background of quantum mechanics, why it's important, how it relates to other branches of knowledge, what it's used for - we just plunge right into imaginary numbers. As implied by the title, the book combines the excitement of matrix algebra with the real-world relevance and practicality of quantum mechanics. If you didn't roll out of bed in the morning thinking "Boy oh boy, here I go learning quantum mechanics!" as your new-years resolution, then this is not the book for you.
This is further compounded by the lack of experiments, diagrams, or even a clear explanation of the physical realities that the book is focused on - it is rather interesting to write a physics book with nothing physical. There's certainly no glossary or answer key or anything helpful like that. For example, the first physics chapter begins "The Pauli Matrices are used to represent the spin angular momentum or magnetic moment of an electron . . ." When I read this line I sighed, uncorked a bottle of wine, and started looking up stuff on Wikipedia - this was clearly going to be one of *those* books.
Finally, there is not only no answer key but also generally no worked examples of the sorts of problems that showed up. My solutions certainly made sense to me, but I have no way of knowing if I did them right or if I somehow learned whole chapters wrong.
This book definitely assumes that the reader is motivated to read an abstract text on quantum mechanics, confident in their math abilities, and has a strong enough physics background that they understand the basics already. I think most people (myself included) would be better served choosing a more accessible text.
The math is *in theory* relatively basic. There's no calculus or differential equations or eigenvectors or any of the revolting mathematics that goes beyond that. This is entirely matrix algebra, and how it can be used to understand quantum mechanics. In particular, the first few chapters provide an excellent review of basic math (complex numbers, matrix operations, etc.) for people who aren't familiar or who have forgotten certain topics. Naturally, problem sets are included at the end of each chapter.
Minus:
For one, the book assumes an engaged and motivated audience. There's no good explanation of the background of quantum mechanics, why it's important, how it relates to other branches of knowledge, what it's used for - we just plunge right into imaginary numbers. As implied by the title, the book combines the excitement of matrix algebra with the real-world relevance and practicality of quantum mechanics. If you didn't roll out of bed in the morning thinking "Boy oh boy, here I go learning quantum mechanics!" as your new-years resolution, then this is not the book for you.
This is further compounded by the lack of experiments, diagrams, or even a clear explanation of the physical realities that the book is focused on - it is rather interesting to write a physics book with nothing physical. There's certainly no glossary or answer key or anything helpful like that. For example, the first physics chapter begins "The Pauli Matrices are used to represent the spin angular momentum or magnetic moment of an electron . . ." When I read this line I sighed, uncorked a bottle of wine, and started looking up stuff on Wikipedia - this was clearly going to be one of *those* books.
Finally, there is not only no answer key but also generally no worked examples of the sorts of problems that showed up. My solutions certainly made sense to me, but I have no way of knowing if I did them right or if I somehow learned whole chapters wrong.
This book definitely assumes that the reader is motivated to read an abstract text on quantum mechanics, confident in their math abilities, and has a strong enough physics background that they understand the basics already. I think most people (myself included) would be better served choosing a more accessible text.
Currently reading
May 12, 2024I have purchased this book over the a booking bearing a similar name (978-3319263649) that is part of Springer's undergraduate Physics lecture series.
This book is ideal to cover grounds on contemporary issues persons face with the framework. Taking the introduction to matrix multiplication as an example—for the case of a rank one tensor, there is so much ambiguity surrounding shaping it to fit a multiplication operation without a constraint on shape. Succinct axioms and definitions in mathematical physics are not just there for context, the "rules" serve as logical railways toward physical evidences that can be approached precisely. I love pure abstractions. But, not when the grammar is ambiguous. This publication gently nudges its readers in a fundamentally mathematically sound direction.
This book is ideal to cover grounds on contemporary issues persons face with the framework. Taking the introduction to matrix multiplication as an example—for the case of a rank one tensor, there is so much ambiguity surrounding shaping it to fit a multiplication operation without a constraint on shape. Succinct axioms and definitions in mathematical physics are not just there for context, the "rules" serve as logical railways toward physical evidences that can be approached precisely. I love pure abstractions. But, not when the grammar is ambiguous. This publication gently nudges its readers in a fundamentally mathematically sound direction.
Displaying 1 - 3 of 3 reviews