# David Skinner: Principles of Quantum Mechanics

This is the site for the Part II course on Principles of Quantum Mechanics, offered to third year maths undergraduates at Cambridge. I will be lecturing this course for the first time in Michaelmas 2017, and the notes will appear here as they become available.

# Contents

**Introduction: PDF File**

Preliminaries. A very brief introduction to classical and quantum mechanics.**Hilbert Space: PDF File**

Definition of Hilbert Space. Dirac notation. Continuum states. Linear operators. Postulates of quantum mechanics. The generalised uncertainty principle.**Transformations and Symmetries: PDF File**

Transformations of states and operators. Spatial translations. Rotations. Translations around a circle. Parity. Time translations. The Heisenberg picture. Symmetries and conservation laws. Dynamics.**Angular Momentum: PDF File**

Angular momentum eigenstates. Rotation of diatomic molecules. Orbital angular momentum. Wavefunctions for orbital angular momentum eigenstates. Spin. SO(3), SU(2) and their representations. The Stern-Gerlach experiment. Precession in a magnetic field.**Composite Systems: PDF File**

The tensor product of Hilbert spaces. Addition of angular momenta. Examples. Identical particles. Pauli's exclusion principle. The Periodic Table. Intrinsic parity and decay processes.**Dynamical Symmetries: PDF File**

The Harmonic oscillator. Raising and lowering operators and SU(3) dynamical symmetry. Angular momentum of the harmonic oscillator. Dynamics of oscillators. Anharmonic oscillations. The Hydrogen atom. The Runge-Lenz operator. SU(2)×SU(2) dynamical symmetry of the gross structure of Hydrogen.**Time Independent Perturbation Theory: PDF File**

An analytic expansion. Fine structure of hydgrogen. The ground state of helium. The quadratic Stark effect. Degenerate perturbation theory. The linear Stark effect. Validity of perturbation theory.**Time Dependent Perturbation Theory: PDF File**

The interaction picture. Fermi's Golden Rule. Atomic transitions and their selection rules. Absorption, stimulated and spontaneous emission of photons.**Interpretation of Quantum Mechanics: PDF File**

Pure and Mixed States. The Density Operator. Reduced density operators for subsystems. von Neumann entropy. Decoherence. The Copenhagen and Many Worlds interpretations.

# Problem Sheets

**Problem Sheet 1: PDF File****Problem Sheet 2: PDF File**

**Problem Sheet 3: PDF File**

**Problem Sheet 4: PDF File**

# Recommended Books

Any good quality Quantum Mechanics textbook will be appropriate for the course. I particularly recommend Weinberg *Lectures on Quantum Mechanics*,
Sakurai *Modern Quantum Mechanics*, Dirac's classic *Principles of Quantum Mechanics* and you might also like to look at Binney & Skinner *The Physics of Quantum Mechanics*. An approach that takes a deeper look at the functional analysis aspects of Quantum Mechanics can be found in Hall *Quantum Theory for Mathematicians*.