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This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures - a fact not usually emphasized in standard physics textbooks - which makes it easy for mathematicians to understand their basic features.
It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
List of contents
From the Contents: Introductory remarks.- Classical Mechanics.- Quantum Theory: General Principles.- Quantum Mechanics of a Single Particle I.- Quantum Mechanics of a Single Particle II.- The Harmonic Oscillator.- The Hydrogen Atom.- Spin.- Many-Particle Systems.- Quantum Statistical Physics.- Physical Theories as Algebraic Systems.- Quantization. The Classical Limit.- Towards Relativistic Quantum Theory.- An Introduction to Quantum Field Theory.- What is Not Treated in This Book.
About the author
Peter Bongaarts taught for many years theoretical and mathematical physics at the University of Leiden, the Netherlands
Summary
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features.
It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
Additional text
“This is a text intended primarily for advanced undergraduate and graduate students in mathematics, and secondarily for physiscs students wanting an introduction to the modern mathematics utilized in quantum mechanics. It has an intentional algebraic flavor that provides a succinct means for comparison between quantum and classical machanics. … The reader could infer that quantum theory, with its axioms, is tidy and has a well-defined mathematical framework.” (Lawrence E. Thomas, Mathematical Reviews, July, 2015)
“This publication provides a quite interesting text book on quantum theory written having in mind advanced undergraduate or graduate students in mathematics, but which can also be a very nice reference text for physics students having an interest in the mathematical foundations of quantum theory.” (Bassano Vacchini, zbMATH 1315.81001, 2015)
Report
"This is a text intended primarily for advanced undergraduate and graduate students in mathematics, and secondarily for physiscs students wanting an introduction to the modern mathematics utilized in quantum mechanics. It has an intentional algebraic flavor that provides a succinct means for comparison between quantum and classical machanics. ... The reader could infer that quantum theory, with its axioms, is tidy and has a well-defined mathematical framework." (Lawrence E. Thomas, Mathematical Reviews, July, 2015)
"This publication provides a quite interesting text book on quantum theory written having in mind advanced undergraduate or graduate students in mathematics, but which can also be a very nice reference text for physics students having an interest in the mathematical foundations of quantum theory." (Bassano Vacchini, zbMATH 1315.81001, 2015)
