Quantum Mechanics: A Mathematical Introduction (Hardcover)

This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.

這本原創且創新的教科書以線性代數方法介紹和解決量子力學問題的獨特觀點，為讀者提供更深入且實用的對當代物理學基礎支柱的理解。通過對導數的分析，提供了對量子力學、希爾伯特空間和薛定諤方程性質的廣泛動機，同時從算子方法的背景下涵蓋了諸如谐振子、旋轉和氫原子等標準主題。還包括現代物理研究基礎的高級主題，如密度矩陣、熵和純度度量。本書針對本科生讀者，提供了對這一極其重要主題的獨特且數學自包含的處理。作者以引人入勝的寫作風格輕鬆引導學生閱讀，並提供了詳盡的詞彙表供參考，以及大量的家庭作業問題來擴展和發展關鍵概念。教師的在線資源包括完整的解答手冊和講義幻燈片。