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.
News: posts on Scholar
Threads weave a path through the collection of articles. They correspond to a course or part of a course.
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.
Exploration of the role of probability in various areas of physics
The physics and mathematics of rotating systems.
The classical theory for oscillations and waves at a second year university level.
In a rotating coordinate system, a free particle moves in a way that appears to be affected by three forces: the centrifugal force, the Coriolis force and the Euler force. These forces arise only from the rotation of the coordinate system.
The description of 2D rotational motion is further developed in analogue to linear dynamics by introducing the rotational equivalents of force, momentum and mass.
The description of 2D rotational motion is developed in analogue to linear kinematics.
A simple review of the notation and some of the expressions for kinematics and dynamics along a line, for classical physics.
The centre of mass of a system of particles is derived as a fictitious point that behaves as if the mass of the entire system where concentrated there. Tricks for finding it are discussed.
The map of phase space of a dynamical system is a really convenient way of summarising the behaviour of a system. In particular it doesn't require a solution to the equations of motion.
The loaded string is a classic problem of coupled oscillators where \(N\) small masses are threaded onto a light string. It makes a nice transition for considering the continuum case and waves.
The continuum limit of the loaded string is derived, arriving at the one dimensional wave equation.
Coupling together two or more oscillators introduces a whole new level of complexity. It turns out that there is a particular way of looking at the system that makes it simple to solve the motion.
When an oscillator is driven at just the right frequency it hits resonance and absorbs energy from the driving. The details of resonance for a driven and damped harmonic oscillator are explored.