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課程名稱 |
量子力學三
Quantum Mechanics (Ⅲ) |
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開課學期 |
109-1 |
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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716新物716 |
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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/1091Phys8011_ |
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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 Electrodynamics, or Maxwell theory, as well as Classical Mechanics, or Action Principle and Hamilton-Jacobi theory, was not changed by the advent of QM. What QM added is that 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 Mechanics. 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 (電力二). |
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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 |
9/14, 16 |
Why/What's AQM; 1-1 Particle & Field; 1-2 Mech. example; 1-3 Scalar field & Lor.inv.,
mu/range, phi/phi*, Conserv. J_mu; 1-4 F_munu, A_mu, Lagr., Lorentz cond., gauge trx |
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第2週 |
9/21, 23 |
1-5 A_mu in QM: AB effect -- A_i physical // 2-1 Rad. field; H ~ h.m.o. in Q-P pair
2-2 2nd quant.; N_op, |0>, |state>, BE stat. 2-3 A_i/H/P_i op.; photon, mass/spin |
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第3週 |
9/28, 30 |
quant. pecul. 2-4 H_int, process & states, absorp. vs (spont.)emiss.; t-dep. perturb.
spont. emiss. (1 -> 2 decay), Golden rule, E1 dipole, higher multipoles, Planck's law |
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第4週 |
10/5, 7 |
2-5 2->2 Scatter, K-H formula, Rayleigh/Thomson/Raman 2-6 Reson. effects: damping
imag. E & Reson. Scatt. 2-7 Dispers. relation: Re/Im forward amp., macro. n & sig_tot |
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第5週 |
10/12, 14 |
D.R. general 2-8 Lamb shift drive QED: Self-energy in QRT; Ansatz: imag. E-level shift;
Q.Rad. rules => "loop"; mass renorm, observed/bare, subtract/add, Lamb-Ex/Bethe-Th |
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第6週 |
10/19, 21 |
3-1 Prob. in RQM 3-2 spin-1/2: Pauli NRQM to Dirac eq, gamma matrices, Hamiltonian
repr. indep 3-3 Simp. Sol.: NR approx. & rel. v/c exp., Thomas/Darwin terms, Del E |
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第7週 |
10/26, 28 |
plane waves, helicity op., orthonormal basis 3-4 Dirac Eq. Covar.: Lorentz trx, parity
phys.pic., positronium-P 3-5 Bilin.Cov.: pseudo/scalar, axial/vector, tensor, Cliff.Algeb. |
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第8週 |
11/2, 4 |
recap, Gordon decomp. & struct. of j_mu, Kusch & g-2, alpha/pi, Stern & mu_N
alpha_k ~v/c 3-6 Heisenb.Rep./eq.mot., const.of motion, spin precess. in stat. mag. |
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第9週 |
11/9, 11 |
spin precess & g-2, veloc.op.&Zitterbewegung & E<0 comp.: freq/ampl, localization
localization & E<0 comp., strong pot. & Klein's paradox 3-8 Central pot.: q.n. kappa |
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第10週 |
11/16, 18 |
kappa & psi_A,B, sep.var => rad.eqs., H-atom & series sol./b.c., E(n',j) eigenvalue
fine struct., spectro order vs NR, grnd w.f., other effects (h.f. struct.-21cm, etc) |
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第11週 |
11/23, 25 |
Mon.: no class
Wed.: 期中考/Midterm |
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第12週 |
11/30, 12/2 |
3-9 Hole theory, Dirac sea/"vac"/爭議, e+; Thomson scatt: seagull as E<0/hole excit.
seagull: contact vs 1/2mc^2 origin, virtual e-e+/Uehling/Z.b., charge-cong. e- <-> e+ |
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第13週 |
12/7, 9 |
3-10 w.f. => 2nd quantiz. by analogy: psi_op, N/H & Q/mom. op., e-/e+ states, b/d&u/v
recap, spin-stat., charge-conj. b <-> d & psi^C, Lagr. of QED 3-11 n & A,Z; n -> p e nu |
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第14週 |
12/14, 16 |
Fermi theory of beta decay: analog of EM; Yukawa's analogy; pi/mu, nu's detection
4-1 hbar=c=1 units 4-2 Int. Rep., S & U-matrix, prob.=1/unitarity/hermiticity, T-matrix |
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第15週 |
12/21, 23 |
4-3 1st order: pot. scatt. spin-1/2, traces; e+e- annih./creat.; Lambda decay 1 -> 2 + 3
4-4 2nd order: e+e- -> gamma gamma: vac-to-vac M.E. of t-orderd prod./e-propagator |
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第16週 |
12/28, 30 |
propagator, i-eps./contour integr., covariance, Compton => FeynRules, e+onium annih.
4-5 Green fn & Feyn-propag., K_F(x,x') property, scatt. "backward" in t, 1st/2nd order |
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第17週 |
1/4, 6 |
4-6 NN -> NN & scalar prop., ee -> ee & photon propagator, spin-proj. & cov. |
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第18週 |
1/11, 13 |
[期末考週] |
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