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課程名稱 |
量子力學三
Quantum Mechanics (Ⅲ) |
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開課學期 |
110-1 |
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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/1101Phys8011_ |
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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.
N.B. This is not a course on Field Theory, and not QED, but a synthesis of QM, CM & CED. |
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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 |
9/22 |
Why/What's AQM; 1-1 Particle & Field; 1-2 Mech. example; 1-3 Scalar field & Lor.inv.; |
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第2週 |
9/27,9/29 |
mu/range, phi/phi*, Conserv. s_mu; 1-4 F_munu, A_mu, Lagr., Lorentz cond., gauge trx
1-5 A_mu in NRQM: AB effect -- A_i physical // 2-1 Rad. field; H ~ hmo in Q-P pair |
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第3週 |
10/04,10/06 |
2-2 2nd quant.; N_op, |0>, |state>, B.E. stat. 2-3 A_i/H/P_i op.; photon, mass/spin
quant. pecul. 2-4 absorp./(spont)emiss., H_int, t-dep. perturb. 1 -> 2 decay, Golden rule |
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第4週 |
10/11,10/13 |
[放假]
E1 dipole, higher multipoles, Planck's law; 2-5 2 -> 2 Scatter: 1st & 2nd order perturb. |
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第5週 |
10/18,10/20 |
K-H formula, Rayleigh/Thomson/Raman 2-6 Reson.Scatt.: damping, imag. E & Reson.
Disp.Rel.: Re/Im forward amp., n & sig_tot, Comment 2-8 Self-energy in QRT, Ansatz |
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第6週 |
10/25,10/27 |
Im DelE & decay; Re DelE & div.; mass renorm, obs/bare, subtr/add, Lamb-E/Bethe-T
3-1 Prob. in RQM 3-2 spin-1/2: Pauli NRQM to Dirac eq, gamma matrices, Hamiltonian |
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第7週 |
11/01,11/03 |
repr. indep. 3-3 Simp. Sol.: NR approx. & rel. v/c exp., Thomas/Darwin terms, Del E
plane waves, helicity op., orthonormal basis 3-4 Covar.: Lorentz trx, parity, phys. pic. |
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第8週 |
11/08,11/10 |
parity 3-5 Bilin.Cov.: pseudo/scalar, axial/vector, tensor, Cliff.Algeb.; Gordon decomp.
g=2, g-2&QED, Stern&mu_N, alpha_k~v/c 3-6 Heisenb.Rep./eq.mot., const. of mot. |
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第9週 |
11/15,11/17 |
11/15 校慶不上課
spin precess. in stat. mag., & g-2, veloc.op./Zitterbewegung & E<0 comp., freq/ampl |
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第10週 |
11/22,11/24 |
11/22 期中考 (Quantum vs Classical radiation, open book)
localization & E<0 comp., strong pot. & Klein's paradox 3-8 Central pot.: q.n. kappa |
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第11週 |
11/29,12/01 |
kappa & psi_A,B, sep.var => rad.eqs., H-atom & series sol./b.c., E(n',j) eigenvalue
E(n',j)&fine struct., spectro order vs NR, grnd w.f., other eff. (h.f. struct.-21cm etc |
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第12週 |
12/06,12/08 |
3-9 Hole theory, Dirac sea/"vac"/爭議, e+; Thomson scatt: seagull as E<0/hole excit.
seagull 1/mc^2 origin, virtual e-e+/Uehling/Z.b.; C.Cong. e- <-> e+ ==> 2nd Quant. |
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第13週 |
12/13,12/15 |
3-10 2nd quantiz. by A_mu analogy: psi_op, N/H/Q/mom_op, e-/e+ states, b/d & u/v
sea 扔了, spin-stat., C.C.: b<->d&psi^C, QED Lagr. 4-1 units 4-2 Int.Rep., S-matrix
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第14週 |
12/20,12/22 |
unitar./hermit., T-mat. 4-3 1st ord.pot.scatt. spin-1/2, traces; e+e- creat.; Lambda decay
1->2+3; 4-4 2nd order: e+e-->gamgam: vac-to-vac M.E. of t-orderd prod./e-propagator |
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第15週 |
12/27,12/29 |
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16週 |
1/03,1/05 |
4-6 NN -> NN & scalar prop.; spin-proj. & photon prop., ee -> ee & trx phot. spin-proj.
cov. phot. prop.; Møller crosssec., QED proc.; V(x) <=> M_fi & App: 核物與膠球束縛態 |
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