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課程名稱 |
量子力學二
Quantum Mechanics (Ⅱ) |
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開課學期 |
112-2 |
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授課對象 |
天文物理研究所 |
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授課教師 |
裴思達 |
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課號 |
Phys7015 |
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課程識別碼 |
222EM1420 |
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班次 |
02 |
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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 |
星期二9,10(16:30~18:20)星期四9,10(16:30~18:20) |
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上課地點 |
新物112新物112 |
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備註 |
本課程以英語授課。
限學號雙號
總人數上限：70人 |
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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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Introductory Course on General Relativity, aiming at advanced undergraduates and beginning graduate students. |
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課程目標 |
Introduction to Differential Geometry, Riemannian Geometry, Einstein Equation and its various solutions, black holes and gravitational waves, applications to cosmology if possible. |
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課程要求 |
Pre-requisites: Classical Mechanics, Electromagnetism, Special Relativity, Partial Differential Equations, knowledge about differential geometry and Lie groups is useful. |
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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 |
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參考書目 |
待補 |
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評量方式
(僅供參考) |
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針對學生困難提供學生調整方式 |
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上課形式 |
以錄影輔助, 提供學生彈性出席課程方式 |
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作業繳交方式 |
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考試形式 |
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其他 |
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週次 |
日期 |
單元主題 |
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Week 1 |
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- Summary of QM-I
- Approximation Methods: Time Independent Perturbation Theory, Non-Degenerate case. |
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Week 2 |
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- Approximation Methods: Time Independent Perturbation Theory, Degenerate case.
- Example1: The Linear Stark Effect |
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Week 3 |
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- Example2: Fine Structure Corrections:
1. Relativistic Correction
2. Spin Orbit Correction
3. Non-Local correction (attempt to introduce in a novel way) |
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Week 4 |
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- Examples: Zeeman effect, PT problems and solutions.
- Lamb shift (if time allows).
- Time dependent Potentials
- Two state system with V(t)
- Spin Magnetic Resonance
- Maser |
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Week 5 |
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- Time dependent Perturbation Theory: Dyson Formula
- Transition probability
- Constant perturbation: Fermi's Golden Rule
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Week 6 |
March-25 |
- Harmonic Perturbation
- Applications to Interactions with the Classical Radiation Field (1)
o Absorption and Stimulated emission
o Gauge Invariance and EM field A - electron current J interaction
- Applications to Interactions with the Classical Radiation Field (2)
o Electric Dipole Approximation
o Photoelectric Effect
o Spontaneous Emission
o Energy shift and Decay shift
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Week 7 |
April 1 |
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Week 8 |
April 8 |
- Scattering Theory (1)
o Definition of the scattering problem
o Solving the t-independent Schrodinger for the scattering problem
o Derivation of the (physical) propagator
o Born Approximation
- Problems and Solutions |
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Week 9 |
April 15 |
- Midterm (April 16th)
- Scattering Theory (2)
o Lippmann-Schwinger Equation, S-matrix, T-matrix
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Week 10 |
April 22 |
o Cross-section
o Optical Theorem
o Born Examples: Yukawa scattering, Rutherford scattering.
o Spherical waves,
o Phase Shifts and Partial Waves
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Week 11 |
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- Scattering Theory (3)
Bound States, Resonance Scattering
- Scattering Theory (4) Other topics
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Week 13 |
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Quantization of the EM field. Maxwell’s Equations
Relativistic QM (1) Klein Gordon Equation |
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Week 14 |
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Relativistic QM (2) Dirac Equation
Relativistic QM (3) Applications. Other topics |
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