Geometric Quantum Mechanics - by Michel Van Veenendaal (Hardcover)

About the Book

"Geometric Quantum Mechanics is a textbook for quantum mechanics at the senior undergraduate and graduate level and follows an approach unique to textbooks in this field. The first chapter starts with the discussion of the properties of space leading to an understanding of operator techniques, Pauli matrices, quantum angular momentum, etc. The second chapter extends this to spacetime. This leads to the Lorentz equation, Maxwell's equations, and the Schrèodinger/Heisenberg equations, linking different fields to each other. Both chapters extensively use geometric algebra. This approach can be used to describe the motion in and production of electromagnetic fields, leading to the Lorentz and Maxwell equations, respectively. The following chapters discuss applications of quantum mechanics. These are subdivided into single-particle problems, many-particle systems, and collective and emergent phenomena. The coverage includes the fundamental forces, molecules and solids, nuclear physics, mass generation and the Higgs field, superconductivity, superfluidity, etc. The book restricts itself to the essence of these topics allowing the reader to understand how quantum mechanics impacts modern-day physics and chemistry. It appeals to instructors and students due to its different approach with its extensive use of geometric algebra and the broad range of modern applications"--

Book Synopsis

Geometric Quantum Mechanics

Unique senior undergraduate/graduate level textbook on quantum mechanics that employs an intuitive, geometry-driven approach to the subject

Geometric Quantum Mechanics is a textbook for quantum mechanics at the senior undergraduate and graduate level and follows a unique approach to the material. The first chapter starts with the discussion of the properties of space leading to an understanding of operator techniques, Pauli matrices, spinors, quantum angular momentum, etc. Techniques from geometric algebra is frequently employed leading to more intuitive insights into the concepts.

The second chapter extends the results to spacetime. The study of the motion in and the production of electromagnetic fields leads to the Lorentz and Maxwell equations, respectively. The nonrelativistic limit leads to the Schrödinger/Heisenberg equations. This provides an overview how different fields are linked to each other.

The following chapters discuss applications of quantum mechanics. This covers a very broad area of physics showing how the ideas from quantum mechanics affect different fields. These are subdivided into chapters on single-particle problems, many-particle systems, and collective and emergent phenomena. The coverage includes the fundamental forces, atoms, molecules and solids, nuclear and particle physics, mass generation and the Higgs field, superconductivity, superfluidity, etc. The book restricts itself to the essence of these topics allowing the reader to understand how quantum mechanics impacts modern-day physics and chemistry. It appeals to instructors and students due to its different approach with its extensive use of geometric algebra and the broad range of modern applications.

From the Back Cover

Unique senior undergraduate/graduate level textbook on quantum mechanics that employs an intuitive, geometry-driven approach to the subject

Geometric Quantum Mechanics is a textbook for quantum mechanics at the senior undergraduate and graduate level and follows a unique approach to the material. The first chapter starts with the discussion of the properties of space leading to an understanding of operator techniques, Pauli matrices, spinors, quantum angular momentum, etc. Techniques from geometric algebra is frequently employed leading to more intuitive insights into the concepts.

The second chapter extends the results to spacetime. The study of the motion in and the production of electromagnetic fields leads to the Lorentz and Maxwell equations, respectively. The nonrelativistic limit leads to the Schrödinger/Heisenberg equations. This provides an overview how different fields are linked to each other.

The following chapters discuss applications of quantum mechanics. This covers a very broad area of physics showing how the ideas from quantum mechanics affect different fields. These are subdivided into chapters on single-particle problems, many-particle systems, and collective and emergent phenomena. The coverage includes the fundamental forces, atoms, molecules and solids, nuclear and particle physics, mass generation and the Higgs field, superconductivity, superfluidity, etc. The book restricts itself to the essence of these topics allowing the reader to understand how quantum mechanics impacts modern-day physics and chemistry. It appeals to instructors and students due to its different approach with its extensive use of geometric algebra and the broad range of modern applications.

About the Author

Michel van Veenendaal, PhD is a Distinguished Research Professor in the Department of Physics at Northern Illinois University, DeKalb, IL, USA and a physicist at Argonne National Laboratory, IL, USA.