Newtonian mechanics describes very well physical phenomena which occur on everyday length and energy scales. Einstein realized that for matter travelling at speeds close to that of light, it is a poor approximation to reality and must be replaced by special relativity. It also slowly became clear from experimental evidence in the early part of this century that Newtonian mechanics and classical electromagnetic theory also fail to provide an adequate description of nature on atomic length scales. Through the work of physicists such as Bohr, Schrödinger, Heisenberg and Dirac, a radical new picture of nature at microscopic scales emerged, in the form of quantum mechanics. This has proven to be an astonishingly successful and powerful theory, and forms the basis of our present understanding of the properties of matter via solid state, molecular, atomic, nuclear and (with the incorporation of relativity) particle physics.

The objective of this course is to provide you with the means to start coming to grips with the world in quantum terms. Physical systems are described by wavefunctions which contain all the information that can be determined about the system by performing measurements. In particular, it is not in general possible to predict the outcome of a measurement of a quantity like position or momentum, but only the probability of various outcomes. Also, the very act of measurement disturbs a system and this places limits on the precision with which quantities like position and momentum can be simultaneously specified, beautifully encapsulated in the Heisenberg uncertainty principle. The Schrödinger equation is the tool which allows the determination of the wavefunction describing a given physical system. The main thrust of the course is therefore toward solving the Schrödinger equation in various physical situations and learning how to extract and interpret the information hidden in the wavefunction. The applications of these ideas to real physical systems is also addressed.