The aim of this module is to give a thorough grounding in the principles of quantum mechanics. It builds on the wave mechanics studied in Years 1 and 2 where the wave nature of matter was introduced as described by the Schrodinger equation. In this module we begin with the fundamental postulates underlying quantum mechanics. We will introduce and consistently use Dirac's notations for doing quantum mechanics which will allow us to study quantum properties like  "spin" which have no counterparts in classical physics. This is vital for applications of quantum mechanics such as quantum computing. We will also see how the Schrodinger equation originates. The module will cover fundamental aspects - such as quantum mechanical postulates - as well as applications and approximate, yet powerful, tools like perturbation theory for handling situations where exact results are not possible.

By the end of the module the student should be able to:

• describe the main postulates of quantum mechanics;
• compute the probabilities of observables and expectation values given a sequence of measurements of a quantum system; use Dirac’s notations;
• use completeness condition;
• use operator commutation relations to compute the time-dependence of expectation values and uncertainty relations;
• use ladder operators for the simple harmonic oscillator and for angular momentum and spin operators ;
• identify and construct non-interacting wavefunctions suitable for indistinguishable fermions and bosons;
• use time-independent perturbation to first and second order.