The following discussion is meant to give some more formalism to students of the Variational Principles course and perhaps tie it to material that they might have come across in analysis or linear algebra courses.

This page is a work in progress and may not be accurate; formulae may have …

This page, which will be updated occasionally, summarises important results and useful formulae for the Part IB Quantum Mechanics course.

Vector spaces, inner products and duality

Let $V$ be an inner product space over $\mathbb{C}$.

We use ket notation for vectors: $|\psi\rangle \in V$

The inner product between …

Here are some notes for my Fluid Dynamics II students about vectors, pseudovectors and how they transform under reflections.

Let n be a unit vector and consider the reflection R in the plane perpendicular to n.

Quantities such as the position r and velocity v are regular vectors and transform …

This is a collection of notes about time and related concepts. A future post will talk about the problems of representing time in computer systems, especially distributed systems. These notes will be occasionally updated.

Introduction

Time is taken to be a primitive concept that cannot be defined in terms of …

In the previous post I discussed how, when measuring the frequency (tempo) of a signal that itself changes in time, there is necessarily a tradeoff between the precision in the measured frequency and precision in the time at which the measurement is taken: A more precise measurement of frequency requires …

Most people are introduced to the term 'uncertainty principle' in the context of quantum mechanics. It is usually described as the idea that a particle's position and momentum cannot be simultaneously measured to arbitrary precision, but that improved precision in one must be traded off against increased uncertainty in the …

This page is intended to give a little context behind the "Bohr model" that is introduced in the first Quantum Mechanics sheet.

Background

Like all atomic models, the Bohr model attempts to answer the question "Why do atoms exhibit the properties that they do?", proposing a mechanical or mathematical description …

What is a variational principle?

A variational principle is a mathematical or physical law expressed in terms of maximising or minimising a certain quantity. The simplest example was known to ancient Egyptian builders and surveyers: a taut rope stretched between two points takes the shape that minimises its length. This …