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週次 |
日期 |
單元主題 |
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Week 1 |
Feb/17 |
- Summary of QM-I
- Approximation Methods: Time Independent Perturbation Theory, Non-Degenerate case. |
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Week 2 |
Feb/24 |
- PT Problems and Solutions
- Approximation Methods: Time Independent Perturbation Theory, Degenerate case.
- Example1: The Linear Stark Effect |
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Week 3 |
Mar/3 |
- 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 |
Mar/10 |
- 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 |
Mar/17 |
- Time dependent Perturbation Theory: Dyson Formula
- Transition probability
- Constant perturbation: Fermi's Golden Rule
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Week 6 |
Mar/24 |
- 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
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Week 7 |
Mar/31 |
- 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
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Week 8 |
Apr/7 |
- Applications to Interactions with the Classical Radiation Field (2)
o Spontaneous Emission
o Energy shift and Decay shift
- Midterm (Thursday Apr/10th)
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Week 9 |
Apr/14 |
- 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
- Scattering Theory (2)
o Lippmann-Schwinger Equation, S-matrix, T-matrix
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Week 10 |
Apr/21 |
o Cross-section
o Optical Theorem
o Born Examples: Yukawa scattering, Rutherford scattering.
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Week 11 |
Apr/28 |
- Scattering Theory (3)
o Spherical waves, Radial solutions, Asymptotic form of Bessel and Neumann functions.
o Phase Shifts and Partial Waves. Partial wave Scattering Matrix, partial wave scattering amplitude
o Determining the Phase shifts.
o Hard-Sphere scattering (low energy limit)
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Week 12 |
May/5 |
- Scattering Theory (4): examples
o High energy limit: the Eikonal Approximation
o Scattering amplitude in the Eikonal Approximation
o Hard-Sphere scattering (Eikonal Approximation)
o Bound States
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Week 13 |
May/12 |
- Scattering Theory (5): Summary
o Analyticity of S-matrix
o Resonance Scattering
- Quantum Fields (Sakurai 7.7)
o Second Quantization Fock Space
o Quantization of the EM field. Maxwell’s Equations
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Week 14 |
May/19 |
- Relativistic QM: Klein Gordon Equation |