Practical Quantum Mechanics: Modern Tools and Applications (Hardcover)

Efstratios Manousakis

  • 出版商: Oxford University
  • 出版日期: 2016-01-12
  • 售價: $1,050
  • 貴賓價: 9.8$1,029
  • 語言: 英文
  • 頁數: 344
  • 裝訂: Hardcover
  • ISBN: 0198749341
  • ISBN-13: 9780198749349
  • 相關分類: 量子 Quantum
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商品描述

Quantum mechanics forms the foundation of all modern physics, including atomic, nuclear, and molecular physics, the physics of the elementary particles, condensed matter physics. Modern astrophysics also relies heavily on quantum mechanics. Quantum theory is needed to understand the basis for new materials, new devices, the nature of light coming from stars, the laws which govern the atomic nucleus, and the physics of biological systems. As a result the subject of this book is a required course for most physics graduate students.

While there are many books on the subject, this book targets specifically graduate students and it is written with modern advances in various fields in mind. Many examples treated in the various chapters as well as the emphasis of the presentation in the book are designed from the perspective of such problems. For example, the book begins by putting the Schrodinger equation on a spatial discrete lattice and the continuum limit is also discussed, inspired by Hamiltonian lattice gauge theories. The latter and advances in quantum simulations motivated the inclusion of the path integral formulation. This formulation is applied to the imaginary-time evolution operator to project the exact ground state of the harmonic oscillator as is done in quantum simulations. As an example of how to take advantage of symmetry in quantum mechanics, one-dimensional periodic potentials are discussed, inspired by condensed matter physics. Atoms and molecules are discussed within mean-field like treatment (Hartree-Fock) and how to go beyond it. Motivated by the recent intense activity in condensed matter and atomic physics to study the Hubbard model, the electron correlations in the hydrogen molecule are taken into account by solving the two-site Hubbard model analytically. Using the canonical Hamiltonian quantization of quantum electrodynamics, the photons emerge as the quanta of the normal modes, in the same way as the phonons emerge in the treatment of the normal modes of the coupled array of atoms. This is used later to treat the interaction of radiation with atomic matter.

商品描述(中文翻譯)

量子力學是現代物理學的基礎,包括原子、核子和分子物理學、基本粒子物理學、凝態物理學。現代天體物理學也在很大程度上依賴於量子力學。量子理論需要用來理解新材料、新設備的基礎,以及來自恆星的光的性質、控制原子核的法則和生物系統的物理學。因此,這本書的主題是大多數物理研究生必修的課程。

儘管有許多關於這個主題的書籍,但這本書專門針對研究生,並以現代各個領域的進展為基礎撰寫。書中的許多例子以及書中的重點呈現都是從這些問題的角度設計的。例如,書的開頭將薛定諤方程放在一個空間離散的格子上,並討論了連續極限,受到哈密頓格子規範理論的啟發。後者和量子模擬的進展促使了對路徑積分形式的引入。這種形式應用於虛時間演化算子,以投影出諧振子的精確基態,就像在量子模擬中所做的那樣。為了展示如何利用量子力學中的對稱性,討論了一維周期性勢能,受到凝態物理學的啟發。原子和分子在平均場的處理中被討論(Hartree-Fock方法),以及如何超越平均場。受到凝態物理學和原子物理學中對研究Hubbard模型的最近活躍的影響,通過解析求解兩個點的Hubbard模型,考慮了氫分子中的電子相關性。利用量子電動力學的正規哈密頓量子化,光子以與原子陣列的正常模式處理中聲子類似的方式出現。這之後用於處理輻射與原子物質的相互作用。