Scholar
Welcome to Scholar. This is an experiment in putting lecture notes online.
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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
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Threads
Threads weave a path through the collection of articles. They correspond to a course or part of a course.

A course on quantum measurement theory aimed at MRes and PhD level.

The classical theory for oscillations and waves, and an introduction to quantum wave mechanics. Pitched at a second year university level.

Exploration of the role of probability in various areas of physics

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.

Exploration of the role of symmetry in physics. Covering topics from the principle of stationary action, Lagrangians, Hamiltonians and Noether’s theorem.

The physics and mathematics of rotating systems.
Recently updated articles

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.

The MerminPeres magic square is a neat demonstration of measurement contextuality.

Projectors are linear operators with the property that the square of the operator is the operator.

Observables and Projective measurements. The Born rule. Expectation and variance of observables and uncertainty principle.

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.

Innerproducts and norms are defined. Equipping a vector space with an innerproduct gives an innerproductspace, and let’s us define bases.

Communication through memoryless static channels will be examined, and in particular using repetition codes to counteract the errors introduced by the channel.

Conditional entropy.

The joint entropy and its properties

Quick introduction to convex sets, convex functions and Jensen’s inequality