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南京大学《狄拉克量子力学原理教程》课件

已有 16764 次阅读 2010-10-20 15:32 |个人分类:未分类|系统分类:教学心得|关键词:学者| 量子力学, 爱因斯坦, 南京大学, 科学方法, 狄拉克

狄拉克确立的量子力学的理论体系是建立在量子态的重叠原理的基础上的。对重叠原理没有深刻的认识，对量子力学就只能够当门外汉，或者槛外人了。

因为本学期南京大学研究生院、物理学院的《高等量子力学》课程由超星学术视频全程录像（公布时的名称《狄拉克量子力学原理教程》），将来要面对全世界的物理学专家，所以本人在讲授量子力学的基本原理时，唯狄拉克马首是瞻，不敢自己胡言乱语。

通过多次仔细阅读狄拉克原著并与别的量子力学教材比较，深感讲清楚量子力学的基本原理是对所有教师的艰巨挑战。狄拉克本人在剑桥大学讲授量子力学课程时，干脆用朗读自己的原著来代替讲课，这当然不是成功的课堂教学行为。

有鉴于自己对我国理科教学的现状的了解，今年本人先期课程中概述了古希腊首创的科学传统（主要是爱因斯坦强调的形式逻辑体系）、文化重生与科学革命（Renaissance and scientific revolution）时期完成的科学方法的创造与历次科学革命中的范式转变(Paradigm shift）。本人确认，没有这些前期准备，不具备 reason、objectivity、logic 这三种主要科学品格和思维能力的基础，是不可能弄懂量子力学的。

课件地址：

http://blog.sina.com.cn/s/articlelist_1616511657_0_1.html

课件 10月19日量子力学没有测不准原理

http://blog.sina.com.cn/s/blog_605a02a90100lx51.html

博主十分希望与科学网的各位网友交流学习量子力学的心得，欢迎批评指正。

2010年研究生院、物理学院双语课《狄拉克量子力学原理教程》授课大纲

Lecture Notes on Dirac's Principles of Quantum Mechanics

Chapter One   Recipe to comprehend and command Quantum Mechanics:
              Paradigm shifts

Section 1.1    Brief history of quantum physics
A. Expeimental discoveries leading to quantum mechanics
B. Theoretical innovations in quantum era

Section 1.2    The Scientific Method
A.  Definition of science as given by Einstein
B.  Greek philosophers ：From Thales to Aristotle
C. Euclidean geometry and formal logical system
D. Renaissance and scientific revolution: From Copernicus to Newton
E. Descartes’ Method of Science: The four precepts
F. The Cartesian geometry

Section 1.3    Review of Classical Mechanics
A. Einstein’s critical review of Newtonian mechanics based on Descartes’
    four precepts
B. The Lagrangian mechanics
C. The Hamiltonian mechanics

Section 1.4    Paradigm and paradigm shifts in scientific revolutions
A. Paradigm in science
B. Paradigm shifts in scientific revolutions

Section 1.5   Paradigm shifts: the recipe to comprehend and command Quantum Mechanics
A. Example one of paradigm shifts in quantum physics: Planck oscillator, from
    c-number to q-number and from visible physical space to abstract
    mathematical space
B. Example two of paradigm shifts in quantum physics: The Stern–Gerlach
    experiment and spin, paradigm of quantum measurement and Pauli matrix
    approach to two-level system

Chapter Two   Dirac's four axioms of Quantum Mechanics: Superposition,
              Observables, Canonical quantization and Equation of motion

Section 2.1   Axiom I：Principle of superposition
A. Definition of quantum states and the general principle of superposition
B. Mathematical formulation of the principle
C. Dirac's notation for vectors: the ket
D. Dirac's introduction of inner product function and bra vectors
E. The dual relationship between ket and bra

Section 2.2   Axiom II：Principle of observables
A. Linear operators （q-numbers）
B. Operator operating on the bra vectors
C. Conjugate relations
D. Eigenvalues，eigenvectors and eigenspace
E. The eigenvalue problem of Hermitian operators
F. Axioms of observables in quantum mechanics and explanation of the  Stern-Gerlach experiment

Section 2.3 Axiom III：Quantization conditions
A. Sequential Stern-Gerlach experiment again
B. Commutability and compatibility
C. Uncertainty relation
D. Axiom of quantization conditions: Dirac canonical quantization
E. Heisenberg uncertainty relation between x and p

Section 2.4   Axiom IV：Equation of motion
A. The Heisenberg equation of motion
B. The Schrödinger equation of motion

Chapter Three   Dirac's three rules of manipulations in Quantum Mechanics:
                Representations, Transformations and Pictures

Section 3.1   Representations of discrete eigenvalue spectra - matrix
A. The basis of a linear vector space and the basis vectors
B. The eigenvectors of Hermitian operators as orthonormal basis of Hilbert
      space
C. The discrete eigenvalue spectra and the matrix representation or matrix
    mechanics
D. Matrix (energy or Heisenberg) representation of Planck oscillator
E. Matrix representation of spin one half and the Stern-Gerlach experiment
     again