Exploring Quantum Physics
开始时间: 04/22/2022
持续时间: Unknown
课程主页: https://www.coursera.org/course/eqp
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课程简介
An introduction to quantum physics with emphasis on topics at the frontiers of research, and developing understanding through exercise.
课程大纲
Week 1 (March 25 -31)
Lecture 1: Introduction to quantum mechanics. Early experiments
- 1.1 Richard Feynman on learning quantum physics and more
- 1.2 Albert Einstein's Nobel prize: photo-electric effect; photons
- 1.3 Explosion in a lab shows electrons are actually waves; electron
diffraction
- 1.4 "Deriving" the Schrödinger equation
- 1.5 Spreading of quantum wave-packets; Heisenberg uncertainty principle
Lecture 2: Interpretation and foundational principles of quantum mechanics
- 2.1 Discussion of Schrödinger's and Born's Nobel prize-winning
works. Probabilistic interpretation of QM
- 2.2 The continuity equation for probability. Probability current
- 2.3 Quantum operators and expectation values
- 2.4 Superposition principle. Dirac notations. Representations
Week 2 (April 1 - 7)
Lecture 3: Feynman formulation of quantum theory
- 3.1 Feynman path integral in a nutshell
- 3.2 Propagator. Time-evolution operator
- 3.3 Formal derivation of the path-integral, part I (difficult material - optional)
- 3.4 Formal derivation of the path-integral, part II (difficult material - optional)
Lecture 4: Using Feynman path integral
- 4.1 Newton's second law of motion "hidden" in the Feynman path integral
- 4.2 Electrical conductivity of a metal - simple classical picture and quantum corrections to it
- 4.3 Quantum (weak) localization. Interference between loop-trajectories
Week 3 (April 8 -14)
Lecture 5: Back to the Schrödinger picture: bound states in quantum potential wells
- 5.1 Quantization in a guitar string and a quantum well. Electron in a box
- 5.2 Electron in a finite potential well. Shallow quantum well
- 5.3 Weakly-bound state in a 1D Dirac delta-potential (shallow well)
- 5.4 Shallow potential in 2D and 3D (difficult material - optional)
Lecture 6: Cooper pairing in the theory of superconductivity
- 6.1 Motivation - superconductivity phenomena: zero resistance, flux
repulsion, levitation
- 6.2 Quantum statistics in a nutshell: fermions and bosons
- 6.3 Electrons in a metal - a simple picture. Fermi surface
- 6.4 Cooper pairing: weakly-bound electron pairs
Week 4 (April 15 - 21)
Lecture 7: Atomic spectra
- 7.1 Atomic spectra. Overview of experimental data
- 7.2 Bohr’s theory of hydrogen atom.
- 7.3 Derivation of the spectrum of hydrogen atom using symmetry arguments.
Lecture 8: Formal solution of the Schrödinger equation in Coulomb potential
- 8.1 Analytical approach
- 8.2 Numerical solution
Week 5 (April 22 -28)
Lecture 9: Symmetry and conservation laws in quantum mechanics
- 9.1 Symmetry in quantum mechanics
- 9.2 Angular momentum, parity,
- 9.3 Discrete symmetries and time-reversal.
Lecture 10: Spin
- 10.1 Stern–Gerlach experiment
- 10.2 Spinors, spin operators, Pauli matrices
- 10.3 Practical applications
Week 6 (April 29 - May 5)
Lecture 11: Harmonic oscillator
- 11.1 Algebraic solution to the harmonic oscillator: Creation and
annihilation operators
- 11.2 Particle in a magnetic field. Landau levels
- 11.3 Quantum Hall effect in a nutshell
Lecture 12: Periodic structures in quantum mechanics
- 12.1 Spherical cow model of a crystal: a chain of harmonic oscillators
- 12.2 Phonons. Goldstone theorem
- 12.3 Electron in a periodic potential. Bands
- 12.4 Topology of the bands. Topological insulators in a nutshell
Week 7: (May 6 - May 12)
Lecture 13: Time-dependent quantum mechanics
- 13.1 Sudden perturbation. Shaking of an atom
- 13.2 Slow perturbations. Topological Berry phase
- 13.3 Spin in a time-dependent magnetic field
Lecture 14: Quantum optics
- 14.1 Introduction to quantum optics
- 14.2 Physics of a laser.
- 14.3 Coherent states
Week 8: (May 13 - May 19)
Lecture 15: Ultra-cold quantum gases
- 15.1 Introduction to ultra-cold atoms
- 15.2 Bose-Einstein condensation
- 15.3 Degenerate Fermi gases
Lecture 16: Summary of the course. Answering student's questions. Outlook
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