週次 |
日期 |
單元主題 |
Week 1 |
|
- Summary of QM-I
- Approximation Methods: Time Independent Perturbation Theory, Non-Degenerate case. |
Week 2 |
|
- Approximation Methods: Time Independent Perturbation Theory, Degenerate case.
- Example1: The Linear Stark Effect |
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) |
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 |
Week 5 |
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- Time dependent Perturbation Theory: Dyson Formula
- Transition probability
- Constant perturbation: Fermi's Golden Rule
|
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 |
Week 9 |
April 15 |
- Midterm (April 16th)
- Scattering Theory (2)
o Lippmann-Schwinger Equation, S-matrix, T-matrix
|
Week 10 |
April 22 |
o Cross-section
o Optical Theorem
o Born Examples: Yukawa scattering, Rutherford scattering.
|
Week 11 |
April 29 |
- 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)
|
Week 12 |
May 6 |
- 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
|
Week 13 |
May 13 |
- 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
|
Week 14 |
May 20 |
- Relativistic QM: Klein Gordon Equation |