This unit looks at quantum mechanics in greater depth than PHYS301 and from a more foundational perspective. After an introduction to the postulated of quantum theory, we consider the basic mathematical structure of quantum mechanics including Hilbert Space, the Dirac notation, linear operators, spectral theory and measurements in quantum mechanics. Tools for the description of multiple systems and statistical combinations of systems are introduced allowing the exploration of entanglement - arguably the most dramatic departure from classical physics. The Harmonic Oscillator is covered in some detail using both the position, momentum and operator methods. In the second half of the unit Quantum Optics is introduced, a topic which has widespread applications, and in this section we cover quantization of the optical field, introduce coherent states and describe the physics behind the quantum interaction of light and atoms.