Linear Algebra for Quantum Theory - by Per-Olov Löwdin Hardcover

Book Synopsis

Essential mathematical tools for the study of modern quantumtheory.

Linear Algebra for Quantum Theory offers an excellent survey ofthose aspects of set theory and the theory of linear spaces andtheir mappings that are indispensable to the study of quantumtheory. Unlike more conventional treatments, this text postponesits discussion of the binary product concept until later chapters, thus allowing many important properties of the mappings to bederived without it.

The book begins with a thorough exploration of set theoryfundamentals, including mappings, cardinalities of sets, andarithmetic and theory of complex numbers. Next is an introductionto linear spaces, with coverage of linear operators, eigenvalue andthe stability problem of linear operators, and matrices withspecial properties.

Material on binary product spaces features self-adjoint operatorsin a space of indefinite metric, binary product spaces with apositive definite metric, properties of the Hilbert space, andmore. The final section is devoted to axioms of quantum theoryformulated as trace algebra. Throughout, chapter-end problem setshelp reinforce absorption of the material while letting readerstest their problem-solving skills.

Ideal for advanced undergraduate and graduate students intheoretical and computational chemistry and physics, Linear Algebrafor Quantum Theory provides the mathematical means necessary toaccess and understand the complex world of quantum theory.

From the Back Cover

Essential mathematical tools for the study of modern quantum theory.

Linear Algebra for Quantum Theory offers an excellent survey of those aspects of set theory and the theory of linear spaces and their mappings that are indispensable to the study of quantum theory. Unlike more conventional treatments, this text postpones its discussion of the binary product concept until later chapters, thus allowing many important properties of the mappings to be derived without it.

The book begins with a thorough exploration of set theory fundamentals, including mappings, cardinalities of sets, and arithmetic and theory of complex numbers. Next is an introduction to linear spaces, with coverage of linear operators, eigenvalue and the stability problem of linear operators, and matrices with special properties.

Material on binary product spaces features self-adjoint operators in a space of indefinite metric, binary product spaces with a positive definite metric, properties of the Hilbert space, and more. The final section is devoted to axioms of quantum theory formulated as trace algebra. Throughout, chapter-end problem sets help reinforce absorption of the material while letting readers test their problem-solving skills.

Ideal for advanced undergraduate and graduate students in theoretical and computational chemistry and physics, Linear Algebra for Quantum Theory provides the mathematical means necessary to access and understand the complex world of quantum theory.

About the Author

PER-OLOV LÖWDIN, PhD, is a professor emeritus at theDepartment of Quantum Chemistry, Uppsala University, Uppsala, Sweden, and Graduate Research Professor Emeritus at the QuantumTheory Project, Department of Chemistry and Physics, University ofFlorida, Gainesville, Florida. He is Editor-in-Chief of Wiley'sInternational Journal of Quantum Mechanics.