# Quantum Theory

## Alexei Gilchrist

3
Quantum

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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This is the beginnings of a series of articles on quantum theory and is the basis of 7 weeks of a course at 3rd year university level.

*Status:* In development. For the moment all the notes are as mindmaps. As time permits they will typeset and added with links appearing below.

**Mindmaps:** /map/quantum-theory/. Many of the maps are 10Mb or more so please be patient. Pinch or control-scroll to zoom, click and drag to pan.

- 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.
- 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.
- Observables and Projective measurements. The Born rule. Expectation and variance of observables and uncertainty principle.
- Projectors are linear operators with the property that the square of the operator is the operator.
- The Mermin-Peres magic square is a neat demonstration of measurement contextuality.