"Lec 1- Introduction to Quantum Mechanics, Probability Amplitudes and Quantum States"In this series of physics lectures, Professor J.J. Binney explains how probabilities are obtained from quantum amplitudes, why they give rise to quantum interference, the concept of a complete set of amplitudes and how this defines a "quantum state". Notes and problem sets here http://www-thphys.physics.ox.ac.uk/people/JamesBinney/lectures.html
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