Geometric Quantum Mechanics (Hardcover)

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.

《幾何量子力學》

《幾何量子力學》是一本針對高年級本科生和研究生的量子力學教科書，採用直觀、以幾何為基礎的方法來介紹這個主題。第一章從討論空間的性質開始，進而理解算子技巧、Pauli矩陣、旋量、量子角動量等。書中經常使用幾何代數的技巧，以提供更直觀的洞察力。

第二章將結果擴展到時空。研究運動和電磁場的產生分別導出了洛倫茲方程和麥克斯韋方程。非相對論極限導出了薛定諤/海森堡方程。這提供了不同領域之間的聯繫概覽。

接下來的章節討論了量子力學的應用。這涵蓋了物理學的廣泛領域，展示了量子力學的思想如何影響不同的領域。這些章節分為單粒子問題、多粒子系統以及集體和新興現象。內容包括基本力、原子、分子和固體、核物理和粒子物理、質量生成和希格斯場、超導性、超流性等。本書專注於這些主題的核心，讓讀者理解量子力學如何影響現代物理學和化學。由於其不同的方法和廣泛的現代應用，這本書受到教師和學生的喜愛。

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.

Michel van Veenendaal博士是美國伊利諾伊州迪卡爾布北伊利諾伊大學物理系的傑出研究教授，也是美國阿貢國家實驗室的物理學家。