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[南京大学物理学院李俊教授2008年高等量子力学课程视频][mp4][640x360]

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文件名:	ZiJingBT.李俊-高等量子力学.torrent
种子名称:	李俊-高等量子力学
信息:	大小: 6.39 GB \| 文件数: 26 \| Info Hash: bc915f5b68b203f8be670d78683c9a2ecb200b3d
类别:	学习 \| 由 fuwocheng (广大站友) 上传于 2010-12-23 13:20:30
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内容简介:	本视频版权归李俊老师所有。仅供学习交流科研所用，请勿用作非法出版、盗版等其他盈利的用途。原来ftp上有巨大的这个课程的视频了，但是下载速度奇慢，而且每一个视频就有2G之巨，不便观看，这边经过我的重新压制，传到紫荆大家交流。这里的视频的内容是课程的上半部分，下半部分我也没有视频源了。李俊老师的百合帐号：higherQM2007 科学相声大师博客网址：http://blog.sina.com.cn/u/1616511657 祝大家高量考试顺利！ 2010年课程大纲如下（待补充）： 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 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 Section 3.2 Transformations A. Spin operators along arbitrary direction and rotation of the basis vectors B. Transformation of representations of discrete eigenvalue spectra C. Infinitesimal spatial displacement and momentum operator D. Finite translation as unitary transformation E. Properties of unitary operator，infinitesimal unitary transformation and Hermitian operator，symmetry and invariance Section 3.3 Representations of continuous eigenvalue spectra A. Normalization of basis eigenvectors of the abstract linear vector space B. Dirac delta function Section 3.4 The coordinate representation and the wave function A. The basis and the wave function B. The representation of momentum operator C. The “matrix elements” of the canonical quantization condition in the coordinate representation D. The eigenfunction of momentum operator Section 3.5 Derivation of stationary state Schrödinger’s wave equation A. The non-relativistic Hamiltonian B. The eigenequation of the Hamiltonian C. The coordinate representation of the eigenequation of the Hamiltonian and the stationary state Schrödinger's wave equation Section 3.6 Solution of eigenfunctions of Planck oscillator A. The wave function of the ground state B. The wave function of all eigenstates Section 3.7 Representations of mixing discrete and continuous eigenvalue spectra Section 3.8 Complete set of dynamical quantities and simultaneous measurement of compatible observables Section 3.9 Pictures and Axiom IV of quantum mechanics -quantum dynamics A. The time evolution of quantum states B. The Schrödinger equation of motion of quantum states C. The Schrödinger picture D. Derivation of the time-dependent Schrödinger wave equation E. The stationary state F. The Heisenberg picture G. The Heisenberg equation of motion of Planck oscillator H. The Ehrenfest theorem I. Conservation laws in quantum mechanics Section 3.10 Coherent states of Planck oscillator A. The coherent state B. The fourth Dirac ladder operators C. Expansion in Heisenberg representation D. Over-completeness E. Non-orthogonality F. The least uncertainty states in QM G. The time-dependent coherent state H. The coherent state Gaussian wave packet Chapter Four Dirac's theory of electron Section 4.1 Dirac equation A. The special theory of relativity B. The four vectors and mass–energy equivalence C. The Klein–Gordon equation D. Derivation of Dirac equation based on the four axioms of QM E. Playing with the Pauli matrices F. Dirac equation in Dirac representation G. Dirac equation in Weyl representation Section 4.2 The motion of a free electron A. The velocity of Dirac electron and zitterbewegung B. The current conservation of a Dirac electron C. Conservation of angular momentum of a Dirac electron and spin D. Complete set of dynamical quantities of Dirac electron and helicity E. The plane wave solution of a free Dirac electron Section 4.3 Dirac sea，Dirac hole and positron A. The concept of Dirac sea based on the Pauli exclusion principle B. The assumption about observables C. The concept of particles in QM D. Dirac's hole theory, concept of aniti-particle and prediction of positron E. The electron-positron pair production Section 4.4 Quantum field theoretical formulation of Dirac hole theory A. The energy of many Dirac electrons as eigenenergy of a new Hamiltonian B. The Fock representation C. The quantum field theoretical Hamiltonian of electrons and positrons D. The second quantization method Section 4.5 The non-relativistic limit of Dirac equation A. A Dirac electron in electromagnetic field B. Eliminating the rest mass of electron C. The Pauli equation D. The magnetic moment of Dirac electron E. The spin-orbit coupling Section 4.6 Covariance of Dirac equation under symmetrical transformations A. Covariance of Dirac equation under Lorentzian and rotational transformations B. Dirac matrix，Dirac algebra and Dirac spinor C. Lorentzian transformations D. Rotational transformation around z axis E. Properties of the coordinate transformation matrices F. Coordinate transformation of Dirac equation G. Direct transformation of Dirac spinor and Dirac matrices H. Combined rotational transformations of Dirac spinor Chapter Five Dirac Picture Section 5.1 Path integral A. Propagator as kernal of time-evolution of wave function B. The moving basis of coordinate representation C. The infinitesimal propagator D. The Feynman path integral E. Path integral of free particle Section 5.2 Green’s function A. Propagator and time-dependent Green’s function B. Differential equation of time-dependent Green’s function C. Time-retarded and time-advanced Green’s function D. Heaviside step function E. Differential equation of time-retarded and time-advanced GF F. Fourier transformation of time-retarded and time-advanced GF G. Green’s functions as coordinate respresentation of Green’s operators Section 5.3 General properties of Green’s function A. Green’s function as resolvant of the eigenenergies B. Analytical behavior of stationary state retarded and advanced Green’s functions C. Dyson’s equation and transition operator Section 5.4 Green’s function method for bound state and scattering state problems A. Zeroth order Green’s functions B. Finding bound state in vanishing potential well by GF method C. Finding elastic scattering states by GF method Section 5.5 Lippmann-Schwinger equation and elastic potential scattering A. Lippmann-Schwinger equation for elastic potential scattering B. The scattering amplitudes of short-range central potential field C. Transition operator and Born approximation D. Orthogonality relations Section 5.6 Dirac picture A. The Dirac（interaction）picture B. Dyson operator and Tomonaga-Schwinger equation C. Dyson series D. The adiabatic ansatz of Born and Fock E. The S-matrix of Wheeler F. Relation between S-matrix and T-matrix G. Fermi Golden rule first derived by Dirac
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