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課程名稱 |
量子力學三
Quantum Mechanics (Ⅲ) |
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開課學期 |
107-1 |
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授課對象 |
理學院 物理學研究所 |
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授課教師 |
侯維恕 |
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課號 |
Phys8011 |
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課程識別碼 |
222 D1430 |
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班次 |
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學分 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一3,4(10:20~12:10)星期三3,4(10:20~12:10) |
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上課地點 |
新物517新物517 |
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備註 |
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1071Phys8011_QM3 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
量子力學三 |
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課程目標 |
We will cover Advanced Quantum Mechanics by J.J. Sakurai (1967). While QM textbooks are many, but just as Jackson is the "classic" for Classical Electrodynamics, and Goldstein is the "classic" for Classical Mechanics, where both are still in use, the AQM book by Sakurai is a classic. What is less known is that Elecdrodynamics, or Maxwell theory, as well as Classical Mechanics, or Action Principle and Hamilton-Jacobi theory, did not get changed by the advent of QM. What QM added is that the Action has a minimal unit, hence discrete.
This course aims at the synthesis of Classical Mechanics, Electrodynamics and Quantum Mechanics, with only a tiny touch on Statistical Mechanis. We would first review classical fields (Chapter 1), then see how the photon emerges when we apply the quantum of action to Electrodynamics, applying generalize coordinates from Classical Mechanics. We then apply this to Quantum Radiation (Chapter 2), and derive all the widely known phenomena, such as Raleigh and Thomson scatterings. Moving away from nonrelativistic systems, such as the atom, we cover Dirac equation and Relativistic Quantum Mechanics (Chapter 3), then move on to cover Covariant Perturbation Theory (Chapter 4), as far as we can go. |
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課程要求 |
attendance, homework, midterm and final exams.
it is preferable that the students have taken 四大力學 already, including classical radiation theory. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Advanced Quantum Mechanics (1967), by J.J. Sakurai |
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參考書目 |
Advanced Quantum Mechanics, by F. Schwabl |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/10,9/12 |
Why/What's AQM; 1-2 Mech.; 1-3 Scalar, Complex Scalar & Conserved J_mu; 1-4 C.E.D.: F_munu, A_mu, Lagrangian, gauge trx., Lorenz cond.; 1-5 A_mu in QM: w.f. with A_i |
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第2週 |
9/17,9/19 |
A-B effect // 2-1 Classical Rad.; Hamiltonian; Canonical Q-P; 2-2 [Q, P] = i hb; Number op., |0> vacuum, general state, BE stat.; 2-3 A_i, H & P_i op.; photon mass/spin; fluct./phase; |
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第3週 |
9/24,9/26 |
[Mon 中秋 假] classical limit; 2-4 H_int, processes & states, absorp., (spont.) emiss.; t-dep. perturb., decay & dipole rad. [Wed 交習題一] |
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第4週 |
10/01,10/03 |
[不上課] |
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第5週 |
10/08,10/10 |
Higher multipoles: M1 and E2; rederive Planck; 2-5 Scattering: gamma + A -> gamma' + B
... [Wed 雙十 假] |
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第6週 |
10/15,10/17 |
K-H formula: Rayleigh/Thomson/Raman; 2-6 Resonance scattering; 2-7 Dispersion relations; Optical Thm; 2-8 Self-energy of point electron, atomic energy level shift (Ansatz), vs free e |
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第7週 |
10/22,10/24 |
[不上課] |
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第8週 |
10/29,10/31 |
1947 Lamb Shift exp 引領 th; Kramers: observed vs bare (renorm: add/subtract); Bethe calc [Wed 不上課] |
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第9週 |
11/05,11/07 |
3-2 Dirac eq: from spin-1/2 K-G eq, gamma matrices & bi-spinor; 3-3 Solutions: NR approx, rel.-exp. (electrostatic), Del E; free particle, orthonormal basis; 3-4 Lorentz covariance |
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第10週 |
11/12,11/14 |
infinit./finite Lorentz trx, parity, physical cases, parity of positronium; 3-5 Cov. Bilinears, pseudo/scalar, axial/vector, tensor, Gordon decomposition & vector current, anom. moment |
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第11週 |
11/19,11/21 |
mu_N, alpha_k & veloc.; 3-6 Heisenberg eq. & const. of motion, spin precess & g-2, vel. op.; 3-7 Zitterbewegung & impact of E<0 states: freq/ampl, localization, Klein's paradox & 2mc^2 |
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第12週 |
11/26,11/28 |
3-8 Central Force, K&kappa, sep. variables, rad. eqs., H-atom & series sol., E-eigen/shift, spectro order vs NR, grnd w.f., other effects (h.f etc); 3-9 Hole theory, Dirac sea, antiparticle |
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第13週 |
12/03,12/05 |
positron, Thomson scattering from Dirac: excite E<0 hole! virtual e-e+ effect, charge-cong. ... [Wed 不上課] |
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第14週 |
12/10,12/12 |
3-10 issue with 1-particle w.f., 2nd quantize psi(x,t) by analogy, N, H, Q, P ops., e-&e+ states; charge-conj. psi^C vs psi, L of QED; 4-1 Nat'l units, naive dim.; 4-2 Int. Rep., U and S-matrix |
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第15週 |
12/17,12/19 |
U/S/T-matrix, prob./unitarity/hermiticity; 4-3 pot. scattering, e+e- annih./creat. [Fermi theory, Yukawa's analogy] Lambda decay; 4-4 2nd order process: e+e- -> gamagama: e-propagator |
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第16週 |
12/24,12/26 |
mom.-space, i-eps. & contour int., covariance, Compton => Feyn. Rules, positronium annih., [J/psi]; 4-5 Green fn & Feynman propagator, property, "backward" in t, 1st order, 2nd order
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第17週 |
12/31,1/02 |
[Mon 調整放假] 4-6 ee -> ee, scalar prop. and Feyn Rules; Moller scatt & (cov.) photon propagator, M_fi & V(x) & Schr. b.s., QED processes |
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第18週 |
1/07, 1/09 |
[期末考: extended take home of Ch. 4 // 「期中考」: guiding Q&A on Ch. 1&2, QRT vs CED] |
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