| 查看: 5909 | 回复: 112 | |||||||||
| 【奖励】 本帖被评价95次，作者pkusiyuan增加金币 75.6 个 | |||||||||
[资源]
量子力学及场论基础（英文）
|
|||||||||
|
Preface page xvii Physical constants xx 1 Basic formalism 1 1.1 State vectors 1 1.2 Operators and physical observables 3 1.3 Eigenstates 4 1.4 Hermitian conjugation and Hermitian operators 5 1.5 Hermitian operators: their eigenstates and eigenvalues 6 1.6 Superposition principle 7 1.7 Completeness relation 8 1.8 Unitary operators 9 1.9 Unitary operators as transformation operators 10 1.10 Matrix formalism 12 1.11 Eigenstates and diagonalization of matrices 16 1.12 Density operator 18 1.13 Measurement 20 1.14 Problems 21 2 Fundamental commutator and time evolution of state vectors and operators 24 2.1 Continuous variables: X and P operators 24 2.2 Canonical commutator [X , P] 26 2.3 P as a derivative operator: another way 29 2.4 X and P as Hermitian operators 30 2.5 Uncertainty principle 32 2.6 Some interesting applications of uncertainty relations 35 2.7 Space displacement operator 36 2.8 Time evolution operator 41 2.9 Appendix to Chapter 2 44 2.10 Problems 52 3 Dynamical equations 55 3.1 Schrödinger picture 55 3.2 Heisenberg picture 57 viii Contents 3.3 Interaction picture 59 3.4 Superposition of time-dependent states and energy–time uncertainty relation 63 3.5 Time dependence of the density operator 66 3.6 Probability conservation 67 3.7 Ehrenfest’s theorem 68 3.8 Problems 70 4 Free particles 73 4.1 Free particle in one dimension 73 4.2 Normalization 75 4.3 Momentum eigenfunctions and Fourier transforms 78 4.4 Minimum uncertainty wave packet 79 4.5 Group velocity of a superposition of plane waves 83 4.6 Three dimensions – Cartesian coordinates 84 4.7 Three dimensions – spherical coordinates 87 4.8 The radial wave equation 91 4.9 Properties of Ylm(θ, φ) 92 4.10 Angular momentum 94 4.11 Determining L2 from the angular variables 97 4.12 Commutator Li, Lj and L2, Lj 98 4.13 Ladder operators 100 4.14 Problems 102 5 Particles with spin ½ 103 5.1 Spin ½ system 103 5.2 Pauli matrices 104 5.3 The spin ½ eigenstates 105 5.4 Matrix representation of σx and σy 106 5.5 Eigenstates of σx and σy 108 5.6 Eigenstates of spin in an arbitrary direction 109 5.7 Some important relations for σi 110 5.8 Arbitrary 2 × 2 matrices in terms of Pauli matrices 111 5.9 Projection operator for spin ½ systems 112 5.10 Density matrix for spin ½ states and the ensemble average 114 5.11 Complete wavefunction 116 5.12 Pauli exclusion principle and Fermi energy 116 5.13 Problems 118 6 Gauge invariance, angular momentum, and spin 120 6.1 Gauge invariance 120 6.2 Quantum mechanics 121 6.3 Canonical and kinematic momenta 123 6.4 Probability conservation 124 ix Contents 6.5 Interaction with the orbital angular momentum 125 6.6 Interaction with spin: intrinsic magnetic moment 126 6.7 Spin–orbit interaction 128 6.8 Aharonov–Bohm effect 129 6.9 Problems 131 7 Stern–Gerlach experiments 133 7.1 Experimental set-up and electron’s magnetic moment 133 7.2 Discussion of the results 134 7.3 Problems 136 8 Some exactly solvable bound-state problems 137 8.1 Simple one-dimensional systems 137 8.2 Delta-function potential 145 8.3 Properties of a symmetric potential 147 8.4 The ammonia molecule 148 8.5 Periodic potentials 151 8.6 Problems in three dimensions 156 8.7 Simple systems 160 8.8 Hydrogen-like atom 164 8.9 Problems 170 9 Harmonic oscillator 174 9.1 Harmonic oscillator in one dimension 174 9.2 Problems 184 10 Coherent states 187 10.1 Eigenstates of the lowering operator 187 10.2 Coherent states and semiclassical description 192 10.3 Interaction of a harmonic oscillator with an electric field 194 10.4 Appendix to Chapter 10 199 10.5 Problems 200 11 Two-dimensional isotropic harmonic oscillator 203 11.1 The two-dimensional Hamiltonian 203 11.2 Problems 207 12 Landau levels and quantum Hall effect 208 12.1 Landau levels in symmetric gauge 208 12.2 Wavefunctions for the LLL 212 12.3 Landau levels in Landau gauge 214 12.4 Quantum Hall effect 216 12.5 Wavefunction for filled LLLs in a Fermi system 220 12.6 Problems 221 x Contents 13 Two-level problems 223 13.1 Time-independent problems 223 13.2 Time-dependent problems 234 13.3 Problems 246 14 Spin ½ systems in the presence of magnetic fields 251 14.1 Constant magnetic field 251 14.2 Spin precession 254 14.3 Time-dependent magnetic field: spin magnetic resonance 255 14.4 Problems 258 15 Oscillation and regeneration in neutrinos and neutral K-mesons as two-level systems 260 15.1 Neutrinos 260 15.2 The solar neutrino puzzle 260 15.3 Neutrino oscillations 263 15.4 Decay and regeneration 265 15.5 Oscillation and regeneration of stable and unstable systems 269 15.6 Neutral K-mesons 273 15.7 Problems 276 16 Time-independent perturbation for bound states 277 16.1 Basic formalism 277 16.2 Harmonic oscillator: perturbative vs. exact results 281 16.3 Second-order Stark effect 284 16.4 Degenerate states 287 16.5 Linear Stark effect 289 16.6 Problems 290 17 Time-dependent perturbation 293 17.1 Basic formalism 293 17.2 Harmonic perturbation and Fermi’s golden rule 296 17.3 Transitions into a group of states and scattering cross-section 299 17.4 Resonance and decay 303 17.5 Appendix to Chapter 17 310 17.6 Problems 315 18 Interaction of charged particles and radiation in perturbation theory 318 18.1 Electron in an electromagnetic field: the absorption cross-section 318 18.2 Photoelectric effect 323 18.3 Coulomb excitations of an atom 325 18.4 Ionization 328 18.5 Thomson, Rayleigh, and Raman scattering in second-order perturbation 331 18.6 Problems 339 xi Contents 19 Scattering in one dimension 342 19.1 Reflection and transmission coefficients 342 19.2 Infinite barrier 344 19.3 Finite barrier with infinite range 345 19.4 Rigid wall preceded by a potential well 348 19.5 Square-well potential and resonances 351 19.6 Tunneling 354 19.7 Problems 356 20 Scattering in three dimensions – a formal theory 358 20.1 Formal solutions in terms of Green’s function 358 20.2 Lippmann–Schwinger equation 360 20.3 Born approximation 363 20.4 Scattering from a Yukawa potential 364 20.5 Rutherford scattering 365 20.6 Charge distribution 366 20.7 Probability conservation and the optical theorem 367 20.8 Absorption 370 20.9 Relation between the T-matrix and the scattering amplitude 372 20.10 The S-matrix 374 20.11 Unitarity of the S-matrix and the relation between S and T 378 20.12 Properties of the T-matrix and the optical theorem (again) 382 20.13 Appendix to Chapter 20 383 20.14 Problems 384 21 Partial wave amplitudes and phase shifts 386 21.1 Scattering amplitude in terms of phase shifts 386 21.2 χl , Kl , and Tl 392 21.3 Integral relations for χl , Kl , and Tl 393 21.4 Wronskian 395 21.5 Calculation of phase shifts: some examples 400 21.6 Problems 405 22 Analytic structure of the S-matrix 407 22.1 S-matrix poles 407 22.2 Jost function formalism 413 22.3 Levinson’s theorem 420 22.4 Explicit calculation of the Jost function for l = 0 421 22.5 Integral representation of F0(k) 424 22.6 Problems 426 23 Poles of the Green’s function and composite systems 427 23.1 Relation between the time-evolution operator and the Green’s function 427 23.2 Stable and unstable states 429 xii Contents 23.3 Scattering amplitude and resonance 430 23.4 Complex poles 431 23.5 Two types of resonances 431 23.6 The reaction matrix 432 23.7 Composite systems 442 23.8 Appendix to Chapter 23 447 24 Approximation methods for bound states and scattering 450 24.1 WKB approximation 450 24.2 Variational method 458 24.3 Eikonal approximation 461 24.4 Problems 466 25 Lagrangian method and Feynman path integrals 469 25.1 Euler–Lagrange equations 469 25.2 N oscillators and the continuum limit 471 25.3 Feynman path integrals 473 25.4 Problems 478 26 Rotations and angular momentum 479 26.1 Rotation of coordinate axes 479 26.2 Scalar functions and orbital angular momentum 483 26.3 State vectors 485 26.4 Transformation of matrix elements and representations of the rotation operator 487 26.5 Generators of infinitesimal rotations: their eigenstates and eigenvalues 489 26.6 Representations of J 2 and Ji for j = 12 and j = 1 494 26.7 Spherical harmonics 495 26.8 Problems 501 27 Symmetry in quantum mechanics and symmetry groups 502 27.1 Rotational symmetry 502 27.2 Parity transformation 505 27.3 Time reversal 507 27.4 Symmetry groups 511 27.5 Dj(R) for j = 1 2 and j = 1: examples of SO(3) and SU(2) groups 514 27.6 Problems 516 28 Addition of angular momenta 518 28.1 Combining eigenstates: simple examples 518 28.2 Clebsch–Gordan coefficients and their recursion relations 522 28.3 Combining spin ½ and orbital angular momentum l 524 28.4 Appendix to Chapter 28 527 28.5 Problems 528 xiii Contents 29 Irreducible tensors and Wigner–Eckart theorem 529 29.1 Irreducible spherical tensors and their properties 529 29.2 The irreducible tensors: Ylm(θ, φ) and Dj(χ) 533 29.3 Wigner–Eckart theorem 536 29.4 Applications of theWigner–Eckart theorem 538 29.5 Appendix to Chapter 29: SO(3), SU(2) groups and Young’s tableau 541 29.6 Problems 548 30 Entangled states 549 30.1 Definition of an entangled state 549 30.2 The singlet state 551 30.3 Differentiating the two approaches 552 30.4 Bell’s inequality 553 30.5 Problems 555 31 Special theory of relativity: Klein–Gordon and Maxwell’s equations 556 31.1 Lorentz transformation 556 31.2 Contravariant and covariant vectors 557 31.3 An example of a covariant vector 560 31.4 Generalization to arbitrary tensors 561 31.5 Relativistically invariant equations 563 31.6 Appendix to Chapter 31 569 31.7 Problems 572 32 Klein–Gordon and Maxwell’s equations 575 32.1 Covariant equations in quantum mechanics 575 32.2 Klein–Gordon equations: free particles 576 32.3 Normalization of matrix elements 578 32.4 Maxwell’s equations 579 32.5 Propagators 581 32.6 Virtual particles 586 32.7 Static approximation 586 32.8 Interaction potential in nonrelativistic processes 587 32.9 Scattering interpreted as an exchange of virtual particles 589 32.10 Appendix to Chapter 32 593 33 The Dirac equation 597 33.1 Basic formalism 597 33.2 Standard representation and spinor solutions 600 33.3 Large and small components of u(p) 601 33.4 Probability conservation 605 33.5 Spin ½ for the Dirac particle 607 34 Dirac equation in the presence of spherically symmetric potentials 611 34.1 Spin–orbit coupling 611 xiv Contents 34.2 K-operator for the spherically symmetric potentials 613 34.3 Hydrogen atom 616 34.4 Radial Dirac equation 618 34.5 Hydrogen atom states 623 34.6 Hydrogen atom wavefunction 624 34.7 Appendix to Chapter 34 626 35 Dirac equation in a relativistically invariant form 631 35.1 Covariant Dirac equation 631 35.2 Properties of the γ -matrices 632 35.3 Charge–current conservation in a covariant form 633 35.4 Spinor solutions: ur(p) and vr(p) 635 35.5 Normalization and completeness condition for ur(p) and vr(p) 636 35.6 Gordon decomposition 640 35.7 Lorentz transformation of the Dirac equation 642 35.8 Appendix to Chapter 35 644 36 Interaction of a Dirac particle with an electromagnetic field 647 36.1 Charged particle Hamiltonian 647 36.2 Deriving the equation another way 650 36.3 Gordon decomposition and electromagnetic current 651 36.4 Dirac equation with EM field and comparison with the Klein–Gordon equation 653 36.5 Propagators: the Dirac propagator 655 36.6 Scattering 657 36.7 Appendix to Chapter 36 661 37 Multiparticle systems and second quantization 663 37.1 Wavefunctions for identical particles 663 37.2 Occupation number space and ladder operators 664 37.3 Creation and destruction operators 666 37.4 Writing single-particle relations in multiparticle language: the operators, N, H, and P 670 37.5 Matrix elements of a potential 671 37.6 Free fields and continuous variables 672 37.7 Klein–Gordon/scalar field 674 37.8 Complex scalar field 678 37.9 Dirac field 680 37.10 Maxwell field 683 37.11 Lorentz covariance for Maxwell field 687 37.12 Propagators and time-ordered products 688 37.13 Canonical quantization 690 37.14 Casimir effect 693 37.15 Problems 697 xv Contents 38 Interactions of electrons and phonons in condensed matter 699 38.1 Fermi energy 699 38.2 Interacting electron gas 704 38.3 Phonons 708 38.4 Electron–phonon interaction 713 39 Superconductivity 719 39.1 Many-body system of half-integer spins 719 39.2 Normal states ( = 0,G = 0) 724 39.3 BCS states ( = 0) 725 39.4 BCS condensate in Green’s function formalism 727 39.5 Meissner effect 732 39.6 Problems 735 40 Bose–Einstein condensation and superfluidity 736 40.1 Many-body system of integer spins 736 40.2 Superfluidity 740 40.3 Problems 742 41 Lagrangian formulation of classical fields 743 41.1 Basic structure 743 41.2 Noether’s theorem 744 41.3 Examples 746 41.4 Maxwell’s equations and consequences of gauge invariance 750 42 Spontaneous symmetry breaking 755 42.1 BCS mechanism 755 42.2 Ferromagnetism 756 42.3 SSB for discrete symmetry in classical field theory 758 42.4 SSB for continuous symmetry 760 42.5 Nambu–Goldstone bosons 762 42.6 Higgs mechanism 765 43 Basic quantum electrodynamics and Feynman diagrams 770 43.1 Perturbation theory 770 43.2 Feynman diagrams 773 43.3 T(HI (x1)HI (x2)) andWick’s theorem 777 43.4 Feynman rules 783 43.5 Cross-section for 1 + 2→3 + 4 783 43.6 Basic two-body scattering in QED 786 43.7 QED vs. nonrelativistic limit: electron–electron system 786 43.8 QED vs. nonrelativistic limit: electron–photon system 789 44 Radiative corrections 793 44.1 Radiative corrections and renormalization 793 xvi Contents 44.2 Electron self-energy 794 44.3 Appendix to Chapter 44 799 45 Anomalous magnetic moment and Lamb shift 806 45.1 Calculating the divergent integrals 806 45.2 Vertex function and the magnetic moment 806 45.3 Calculation of the vertex function diagram 808 45.4 Divergent part of the vertex function 810 45.5 Radiative corrections to the photon propagator 811 45.6 Divergent part of the photon propagator 813 45.7 Modification of the photon propagator and photon wavefunction 814 45.8 Combination of all the divergent terms: basic renormalization 816 45.9 Convergent parts of the radiative corrections 817 45.10 Appendix to Chapter 45 821 Bibliography 825 Index 828 |
回复此楼» 本帖附件资源列表
-
欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：libolin3@tal.com - 附件 1 : 量子力学及场论基础.pdf
2015-03-27 14:21:24, 14.38 M
» 收录本帖的淘贴专辑推荐
 精华网帖收集 | 电子书资源 | 制药工程 | 李的收藏 |
| 专业文件-物理卷 | 图书 | 介电材料 |
» 本帖已获得的红花（最新10朵）
考研的爱德华» 猜你喜欢
TsCl保护羟基为什么不反应
已经有26人回复
-
共同通讯谁投稿？
已经有7人回复
-
优秀毕业论文 指导教师，普通老师有希望吗？
已经有11人回复
-
博士复试，申请成绩复核，有机会翻盘吗？
已经有23人回复
-
经常觉得挺累的
已经有16人回复
-
蹲一个男朋友
已经有54人回复
-
人生
已经有11人回复
-
女博士高校择业三天之内签合同，求支招
已经有33人回复
-
答辩
已经有8人回复
-
审不上青基又非升即走的青椒 和 牢里踩缝纫机的犯人哪个活的更舒服一点？
已经有22人回复
» 本主题相关价值贴推荐，对您同样有帮助:
- 送给小白的量子力学学习书-漫画量子力学
已经有240人回复
- 量子力学中的动量算符竟是如此复杂
已经有31人回复
- 论量子力学的一些问题
已经有27人回复
- 量子力学的数学基础（冯诺依曼）英文件版
已经有220人回复
- 场论与张量基础
已经有142人回复
- 高等量子力学习题 求解 相对论量子力学
已经有32人回复
- 数学物理方法与四大力学的学习顺序
已经有24人回复
- 量子力学课后习题答案集（包含了国内的几个著名版本）
已经有234人回复
- 关于量子力学和量子场论的关系的一系列疑问
已经有31人回复
- 求助：量子力学中几率流密度的问题
已经有9人回复
- 关于量子力学中角动量算符的一个疑问
已经有44人回复
- 有虫友知道哪些sci杂志能刊发基础数学代数学方向的文章的投稿，
已经有4人回复
- 王正行的《简明量子场论》
已经有117人回复
- 谁对量子力学的贡献最大？
已经有81人回复
- 高等量子力学(第三版)[杨泽森]
已经有89人回复
- 【求助】问几个关于量子力学的基本问题
已经有11人回复
- 【交流】量子力学教学现状杂谈
已经有49人回复
- 【交流】如何深刻理解量子力学
已经有37人回复
30楼2015-04-01 18:11:32
37楼2015-04-07 23:33:37
39楼2015-04-08 19:52:20
简单回复
2015-03-27 16:26
回复
五星好评 顶一下，感谢分享！
2015-03-30 17:05
回复
五星好评 顶一下，感谢分享！
2015-03-31 04:44
回复
五星好评 顶一下，感谢分享！
YHW20165楼
2015-03-31 06:20
回复
五星好评 顶一下，感谢分享！
Quan.6楼
2015-03-31 06:58
回复
五星好评 顶一下，感谢分享！
吠陀7楼
2015-03-31 07:00
回复
五星好评 顶一下，感谢分享！
wjy20118楼
2015-03-31 07:48
回复
五星好评 顶一下，感谢分享！
2015-03-31 08:18
回复
五星好评 顶一下，感谢分享！
shujj10楼
2015-03-31 09:56
回复
五星好评 顶一下，感谢分享！
gh_wang200811楼
2015-03-31 10:51
回复
五星好评 顶一下，感谢分享！
lichar233312楼
2015-03-31 11:08
回复
五星好评 顶一下，感谢分享！
lexybuaa13楼
2015-03-31 11:24
回复
五星好评 顶一下，感谢分享！
花尽无花14楼
2015-03-31 11:27
回复
五星好评 顶一下，感谢分享！
kuangpan15楼
2015-03-31 11:58
回复
五星好评 顶一下，感谢分享！
孟小硕16楼
2015-03-31 13:06
回复
五星好评 顶一下，感谢分享！
ha166817楼
2015-03-31 16:15
回复
五星好评 顶一下，感谢分享！
zfm1681018楼
2015-03-31 18:20
回复
五星好评 顶一下，感谢分享！
NOSURE19楼
2015-03-31 19:51
回复
五星好评 顶一下，感谢分享！
zao_fan20楼
2015-03-31 20:18
回复
五星好评 顶一下，感谢分享！
xiang67621楼
2015-03-31 20:38
回复
五星好评 顶一下，感谢分享！
happyfishs22楼
2015-03-31 21:27
回复
五星好评 顶一下，感谢分享！
parkzhu23楼
2015-04-01 01:53
回复
五星好评 顶一下，感谢分享！
wsz1024楼
2015-04-01 06:48
回复
五星好评 
gxqh25楼
2015-04-01 09:03
回复
五星好评 顶一下，感谢分享！
journeyer26楼
2015-04-01 10:06
回复
五星好评 顶一下，感谢分享！
gate_open27楼
2015-04-01 11:37
回复
五星好评 顶一下，感谢分享！
cheuecust28楼
2015-04-01 13:56
回复
五星好评 顶一下，感谢分享！
yanjia2000629楼
2015-04-01 14:36
回复
五星好评 顶一下，感谢分享！
starlan31楼
2015-04-01 19:11
回复
顶一下，感谢分享！
licro32楼
2015-04-01 19:59
回复
五星好评 顶一下，感谢分享！
surgen253133楼
2015-04-01 20:39
回复
五星好评 顶一下，感谢分享！
cg3344_134楼
2015-04-01 21:52
回复
五星好评 顶一下，感谢分享！
congyu_200735楼
2015-04-02 12:13
回复
五星好评 顶一下，感谢分享！
wanlingyun36楼
2015-04-03 22:46
回复
五星好评 顶一下，感谢分享！
meixiangling38楼
2015-04-08 07:53
回复
五星好评 顶一下，感谢分享！
有歌无词40楼
2015-04-09 09:17
回复
五星好评 顶一下，感谢分享！
fanxuanji41楼
2015-04-11 22:11
回复
五星好评 顶一下，感谢分享！
victorzhouy42楼
2015-04-13 09:50
回复
五星好评 顶一下，感谢分享！
zjinz43楼
2015-04-19 19:03
回复
三星好评 感谢分享 [ 发自手机版 http://muchong.com/3g ]
bobo071944楼
2015-04-22 13:06
回复
五星好评 顶一下，感谢分享！
wanglc45楼
2015-04-23 08:46
回复
五星好评 顶一下，感谢分享！
beannut200146楼
2015-04-25 16:40
回复
五星好评 顶一下，感谢分享！
feiliping47楼
2015-05-04 13:18
回复
顶一下，感谢分享！
hudi131948楼
2015-05-04 19:26
回复
顶一下，感谢分享！
long_89011549楼
2015-05-06 17:22
回复
五星好评 顶一下，感谢分享！
yonggepy50楼
2015-05-07 09:50
回复
五星好评 顶一下，感谢分享！
10