Scholar
Welcome to Scholar. This is an experiment in putting lecture notes online.
It's a work in progress and material is being added and improved all the time.
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I teach or have taught a variety of courses in physics including classical physics, advanced quantum theory, and advanced physics units on probability and symmetry in physics
News: posts on Scholar
Threads
Threads weave a path through the collection of articles. They correspond to a course or part of a course.
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A course on quantum measurement theory aimed at MRes and PhD level.
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The classical theory for oscillations and waves, and an introduction to quantum wave mechanics. Pitched at a second year university level.
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Exploration of the role of probability in various areas of physics
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A course on quantum theory, concentrating on the structure of quantum mechanics as a basis of physical theory rather than the quantum physics of particular systems. We take a Hilbert space approach.
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Exploration of the role of symmetry in physics. Covering topics from the principle of stationary action, Lagrangians, Hamiltonians and Noether’s theorem.
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The physics and mathematics of rotating systems.
Recently updated articles
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The description of physical states as vectors in a Hilbert space can be extended to a probabilistic description when we don’t have complete information. It turns out we are forced to use such a description in certain situations.
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The Mermin-Peres magic square is a neat demonstration of measurement contextuality.
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Projectors are linear operators with the property that the square of the operator is the operator.
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Observables and Projective measurements. The Born rule. Expectation and variance of observables and uncertainty principle.
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Quantum mechanics can be encapsulated by a set of postulates. In this set we will take the Hilbert space \(\mathcal{H}\) as the primary object.
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Inner-products and norms are defined. Equipping a vector space with an inner-product gives an inner-product-space, and let’s us define bases.
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Communication through memory-less static channels will be examined, and in particular using repetition codes to counteract the errors introduced by the channel.
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Conditional entropy.
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The joint entropy and its properties
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Quick introduction to convex sets, convex functions and Jensen’s inequality