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所在平台: Coursera 课程类别: 物理 |

课程主页: https://www.coursera.org/course/eqp

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Quantum physics is the foundation for much of modern technology, provides the framework for understanding light and matter from the subatomic to macroscopic domains, and makes possible the most precise measurements ever made. More than just a theory, it offers a way of looking at the world that grows richer with experience and practice. Our course will provide some of that practice and teach you "tricks of the trade" (not found in textbooks) that will enable you to solve quantum-mechanical problems yourself and understand the subject at a deeper level.

The basic principles of quantum physics are actually quite simple, but they lead to astonishing outcomes. Two examples that we will look at from various perspectives are the prediction of the laser by Albert Einstein in 1917 and the prediction of antimatter by Paul Dirac in 1928. Both of these predictions came from very simple arguments in quantum theory, and led to results that transformed science and society. Another familiar phenomenon, magnetism, had been known since antiquity, but only with the advent of quantum physics was it understood how magnets worked, to a degree that made possible the discovery in the 1980’s of ultrastrong rare-earth magnets. However, lasers, antimatter and magnets are areas of vibrant research, and they are all encountered in the new field of ultracold atomic physics that will provide much of the material of “Exploring Quantum Physics”.

Richard Feynman once said, “I think I can safely say that nobody understands quantum mechanics.” We say, that’s no reason not to try! What Feynman was referring to are some of the “spooky” phenomena like quantum entanglement, which are incomprehensible from the standpoint of classical physics. Even though they have been thoroughly tested by experiment, and are even being exploited for applications such as cryptography and logic processing, they still seem so counterintuitive that they give rise to extraordinary ideas such as the many-world theory. Quantum physics combines a spectacular record of discovery and predictive success, with foundational perplexities so severe that even Albert Einstein came to believe that it was wrong. This is what makes it such an exciting area of science!

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

- 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)

- 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)

- 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.

- 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.

- 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

- 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

- 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

An introduction to quantum physics with emphasis on topics at the frontiers of research, and developing understanding through exercise.

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