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量子力学前沿选题课程列表:

Chapter 1 The second quantizaton

-S1.1 Algebraic method of solving the 1D harmonic oscillator eigenproblem(1).

-S1.1 Algebraic method of solving the 1D harmonic oscillator eigenproblem(2)

-S1.2 Particle number representation, particle creation & annihilation operators

-S1.3 Change of basis and dynamical variables S1.4The continuous one-particle spectrum

-S1.4 The continuous one-particle spectrum S1.5 Quantum dynamics: Time evolution

-S1.6 Density matrix & 2-particle correlation function for non-interacting Bose & Fermi gas

-S1.7 BCS wave function, Bogolinbov transformation and quasiparticle excitation(1)

-S1.7 BCS wave function, Bogolinbov transformation and quasiparticle excitation(2)

-S1.7 BCS wave function, Bogolinbov transformation and quasiparticle excitation(3)

-Homework1

Chapter 2 The Dirac Equation

-Dirac Equation

Chapter 3 The path Integral Formalism

-S3.1 The propagator

-S3.2 The evaluation of path integral

-S3.3 Example: harmonic oscillator problem solved by path integral

- S3.4 Density matrix & path integral S3.5 Density matrix in statistical mechanism

-S3.6 Path integral for oscillator recalculated

-Homework 3

Chapter 4 Wave-particle Dual Nature & Complementarity

-§4.1 Formation of interference pattern in a double slit experiment with electrons

-S4.2 Direct Demonstration of the Complemetarity Principle by Atomic interferometry (1)

-S4.2 Direct Demonstration of the Complemetarity Principle by Atomic interferometry (2)

-S4.3 Single photon interference experiment S4.4 Multi-particle interferometry

-S4.5 Two-photon interferometer as a quantum eraser S4.6 EPR paradox & Bell theorem(1)

-S4.6 EPR paradox & Bell theorem(2)

-S4.6 EPR paradox & Bell theorem(3)

-S4.7 Experimental Verification of Bell inequality

-Homework4

Chapter 5 Geometry Phase in Quantum Mechanism

-S5.1 Geometrical phase in quantum mechanism(1)

-S5.1 Geometrical phase in quantum mechanism(2)

-S5.2 Experimental Verification of the Aharonov- Bohm effect S5.3 The Abaronov-Casher effect

-S5.4 Parallel Transport, Connexion, Curvature & Anholonomy

-S5.5 The Berry phase(1)

-S5.5 The Berry phase(2)

-Homework5

Chapter 6 Border between Quantum and Classical Mechanics, Entanglement & Decoherence

-S6.1 Schroedinger's harmonic oscillator wave packet S6.2 Coherent states

-S6.3 Circular orbit wave packet of H atom S6.4 SO(4) Dynamical symmetry of H atom

-S6.5 Principle of superposition and the quantum decoherence

-S6.6 Decoherence caused by interaction with environment

-S6.7 Schrödinger’s cat realized in the laboratory

-S6.8 Wave function with a macroscopic significance

-Homework6

Chapter 7 Topological Phase Factor in Quantum Systems

-S7.1 Spin wave theory in Heisenberg model

-S7.1 Spin wave theory in Heisenberg model(2)

-S7.3 1D quantum AFM chain & Topological phase factor

-S7.4 Lieb-Schultz-Mattis theorem

-S7.5 Significance of topological term

-Homework7

Chapter 8 Introduction to Cavity QED

-S8.1 Interaction between radiation fields & the atom(1)

-S8.1 Interaction between radiation fields & the atom(2)

-S8.2 The Jaynes-Cummings model S8.3 Suppression & Enhancement of spontaneous

-S8.5 Inverse Stern-Gerlach Effect S8.6 The atom-cavity dispersive phase shift effect

-S8.7 Ramsey interferometer: the atomic clock

-S8.8 Detecting photons with a Rydberg clock S8.9 Schrodinger cat and decoherence S8.10 The Dark sta

-S8.11 Dicke Model and Phase Transitions(1)

-S8.11 Dicke Model and Phase Transitions(2)

-S8.11 Dicke Model and Phase Transitions(3)

-S8.11 Dicke Model and Phase Transitions(4)

-Homework8

Chapter 9 Quantum Hall Effect

-S9.1 Quantum Hall: Classical S9.2 Electrons in uniform magneti field, the Landau level

-S9.2 2D problem under strong magnetic field

-S9.3 The integer quantum Hall effect(1)

-S9.3 The integer quantum Hall effect(2)

-S9.3 The integer quantum Hall effect(3)

-S9.4 The fractional quantum Hall effect

-S9.4 Quantum anomalous Hall effect(1)

-S9.4 Quantum anomalous Hall effect(2)

-S9.5 Quantum spin Hall effect

-Homework9

Chapter 10 Bose-Einstein Condensation

-S10.1 Introduction S10.2 Order parameter and phsae coherence(1)

-S10.2 Order parameter and phase coherence(2)

-S10.3 Gross-Pitaevskii equation, ground state and excitations

-S10.4 The superfluid face of BEC

-S10.5 BEC in double Well & Josephson effect

-S10.6 Quantum phase transition

-Homework10

S5.5 The Berry phase(1)笔记与讨论

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