Quantum Mechanics: The Harmonic Oscillator and the Wavefunctions of its Stationary States (Lecture 8 of 27) Oxford University

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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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