Linear Algebra for Quantum Theory

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.

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.

PER-OLOV L?WDIN, PhD, is a professor emeritus at the Department of Quantum Chemistry, Uppsala University, Uppsala, Sweden, and Graduate Research Professor Emeritus at the Quantum Theory Project, Department of Chemistry and Physics, University of Florida, Gainesville, Florida. He is Editor-in-Chief of Wiley's International Journal of Quantum Mechanics.