Foundations of Quantum Mechanics
University of Colorado Boulder
This is a challenging course. If you are serious about learning quantum mechanics, I highly recommend this course to you. Furthermore if you want to engage yourself with quantum computing, this course is an excellent choice to lay the foundations.
Your quest starts here: the time-independent Schrödinger equation and Hilbert space. It sounds a little overwhelming, but it won’t be too much, had you obtained solid skills in Matrix Algebra, Differential Equations and Vector Calculus.
Armed with these knowledges, your first challenge is a series of important and practical problems: finite potential well, harmonic oscillator, potential barrier, etc. Then, let’s have some fun: the celebrated Stern-Gerlach Experiments. Meanwhile, you learn the “language”: Dirac Bra-ket Notation. It definitely pays to spend some time on it.
You will next dive into a few concepts: the commutation of operators, the uncertainty principle, and change of basis. These are really the details, but you will recognize their value in the future. When time evolution is considered, the situations become more complicated. Lastly, the ensemble and indistinguishability are covered. I also found an excellent elaboration of boson and fermion in the last chapter.
Remember there are so many things in the micro-world that you won’t find counterpart or analogue in the world you are familiar with. The key to enter the micro-world is to free your mind.
This is a challenging course. If you survived, you’ve got the key! Congratulations! You shall be proud of yourself! ?
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