## About Physics -- First Half the Year

In January, I finished **8.04x, Quantum Mechanics****,** an online course provided by MITx and got perfect grades, 92, 94, and 88 for three exams. 8.04x was lectured by Professor Barton Zwiebach, whose doctoral advisor is Murray Gell-mann. This course introduced basic concepts of Quantum Mechanics and did standard 1-D potential examples, such as square wells, Dirac-delta potential and harmonic oscillators, along with several important theorems for 1-D potential. Besides, it gave a detailed treatment on scattering states in 1-D, covering topics like time delay, Levinson’s theorem and resonance. The course ended with central potential and Hydrogen Atom. It was a challenging but rewarding course, and of course, interesting! What makes this course stand out among all other online courses is its active discussion forum. I met lots of interesting physics and math geeks there, Mark, Jolyon, Jim, BlueFlow and Jonathan, and the discussion about physics with them made my learn experience vivid and lovely (Actually, I read their discussions in forum most of the time). Later in September 2018, Jim offered me an unexpected research experience, which was the first time I worked with a real physicist!

February is holiday season in China, I finished Jacob Linder’s video lectures on **Classical Mechanics**, based on Goldstein’s book. Jacob Linder walked you through Goldstein’s book step by step, demonstrating many examples, so you could learn to do these calculations with him. However, since I’ve learned much about Mechanics in Mechanic Engineering courses in my home institute and want to learn more about Lagrangian and Hamiltonian Formulations. it turned out that this course was too introductory for me. It didn’t go much deep in these two formulations and the problem sets were not quite challenging. I would recommend this course to those who learned classical mechanics for the first time. In addition, I tried **8.370x, Quantum Information Science**, provided by MITx. This course was not as excellent as 8.04x, so I only finished the first part. I planed to study quantum information theory after finishing 8.04 – 8.06 series.

The spring semester in my home institute started in March, as did the continuation Quantum Mechanics course **8.05x, Mastering Quantum Mechanics**. 8.05x started by reviewing key theorems for 1-D potential. The treatment was more systematic and rigorous than 8.04x. After introducing the mind-boggling Stern-Gerlach experiment that demonstrated the quantum mechanical nature of nature, it continued to give rigorous explanation of operators and vector space followed by Dirac’s bra and ket notation. After the training of the first half part of 8.05x, your mind would be quite familiar about operators and vectors. The remaining part focused on the application of operator and algebraic method on examples like harmonic oscillators and angular momentum. Coherent state and squeeze state were also introduced, which is kind of introduction to quantum optics.

My feeling was that 8.05x was not as difficult as 8.04x. It represented the same idea of quantum mechanics using operator and algebraic approach, which I think is much superior to differentiation and integration approach. The important information can be encapsulated compactly into the algebraic relation of operators (or more specific, commutators) and the derivation will be mostly algebra manipulation, which is much easier and more straightforward than dealing with differentiation and integration. Remember how the algebraic method for harmonic oscillator works like magic, and the calculation of related expectation values will be quite trivial using abstract states, annihilation and creation operators, without requiring any specific representation in position or momentum space.**6.041x, Introduction to Probability: Part 2 – Inference and Processes**, ran in parallel with 8.05x. It was second part of MIT’s probability course, covering Bayesian inference, various limit theorems, classical statistics, Poisson and Bernoulli processes, and Markov chains. The problem sets of this course were very interesting. You need to think a little before doing the calculation. These problems were good tests of whether you really understand the key concepts or not, and they were not just plug-in-and-calculate kind of questions.

Apart from these edX MOOCs, I also did **Ph12c, Statistical Mechanics**, lectured by Professor Preskill. It’s an introductory course in statistical mechanics taken by Caltech undergraduates. I mostly relied on the class’s web page, where the lecture videos, lecture notes, problem sets and solutions, exam and solutions are all provided. This is ideal for an independent learner. The lectures followed closed the textbook *Thermal Physics *by Kittel. This course starts with statistical mechanics, and introduces the microscopic definition of important concepts like temperature and entropy at a very early stage, followed by the all important Boltzmann distribution and Gibbs distribution along with classical examples like ideal gas, photon gas, Fermi gas and Bose-Einstein condensation. The abstract thermodynamic definition of temperature and entropy doesn’t come until midway through the course. Professor Preskill is an excellent teacher and it’s a pleasure to have him explain physics to you. I guess the legacy of Feynman affects him a lot. When he came to Caltech to do particle physics, Feynman was at his 60s, and they had several interactions. Preskill’s graduate advisor is Steven Weinberg, another great mind. Now Preskill’s research interests are quantum computation and quantum information theory. I plan to study his lecture notes on quantum computations in the future.

## About Physics -- Second Half of the Year

Second half of 2018 is quite busy. On the one hand, I need to prepare for my physics GRE and my physics application documents. On the other hand, I started a research project with Professor Jim Freericks I met in 8.04x and 8.05x. Walter, a fellow student in 8.05x, told me a **research opportunity with Jim** on September 2018, and then, Jim, a student in Georgetown and I started the research shortly afterwards. All the calculations were finished at the end of December 2018 and Jim finished the first draft one month later.

Working with Jim is a pleasant and rewarding experience. He was always there when I had difficulty understanding some calculations or concepts. He was patient and would work you through every technical details if I saw them for the first time. Although he tended to work way faster than I did (after all he is an experienced physicist!), he would become busy from time to time, so I could have opportunity to catch up! I became more comfortable with complicated algebra manipulations during the research, and started to have a more physicists’ mind set. Unsolved problems could look dirty and messy at the beginning, but we physicists are never scared off if they are interesting and important. Things tend to become elegant and simple when you solve them piece by piece. I enjoy this process.

Jim is now recruiting fellow MOOCers to work on different research projects. He works on quantum mechanics pedagogy, quantum computing, and the non-equilibrium many-body problem. I guess the projects he works with MOOCers are mainly related to his book called *Quantum Mechanics without Calculus, *where he tries to do quantum mechanics in a representation-free fashion, that is, not relying heavily on coordinate space representation, bur rather construct the discrete spectrum algebraically. If you want to know some details about this method, here is Jim’s 8.06x term paper, *Coordinate-space wavefunctions for the simple harmonic oscillator via algebraic operator methods*.

For ordinary physics study, I finished Ph106c: Classical Electrodynamics, given by Professor Sunil Golwala from Caltech. The problems and solutions are not available from internet without Caltech’s IP address. I use its course schedule and the detailed lecture notes. The course textbook is Griffiths’s *Introduction to Electrodynamics, *and Jackson’s *Classical Electrodynamics. *I only went through Griffiths’s textbook. This course is a continuation of 8.02, and emphasize advanced mathematical techniques which are necessary for partial differential equations. You also need to work heavily with vector calculus in this course. All essential techniques in theoretical physics.

Oxford kindly recorded a course on solid state physics called *The Oxford State Basics, *lectured by Professor Steven H. Simon. The sequence of the lectures matches that of the book *The Oxford Solid State Basics* written by Prof. Simon. This is an excellent introductory-level condensed matter physics course. And it can be taken once you finish your undergraduate-level quantum mechanics course, or equivalently 8.04x – 8.06x series provided by MITx. Prof. Simon is a funny teacher and his enthusiastic is infectious! The assignments of this course are the same as the exercises in the book and you can find the solution manual of the book on the internet.

## Non-physics work

Nothing quite interesting, just routine work in structure engineering graduate school. I spent lots of time to improve my work on prediction of the hysteresis curve of RC columns. A lot of details were added to the hysteresis model and in turn more work was needed to be done in the prediction equation. A phenomenology approach was adopted, with no concern about mathematical structure, not quite interesting as far as I could see. But the resultant prediction equation based on 19 shear-critical columns do look satisfactory from an engineer’s perspective. However, from a physicist’s point of view, the work is hard but trivial, just too complicated to give nice results. Structure Engineering isn’t really my game, not where my passion lies.

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