Outline of course

Part I of this course is devoted to an in-depth exploration of the basic ideas of quantum mechanics. As is well-known, the fundamental concepts and axioms of quantum mechanics--the physical theory which governs the behaviour of microscopic dynamical systems (e.g., atoms and molecules)--are radically different to those of classical mechanics--the theory which governs the behaviour of macroscopic dynamical systems (e.g., the solar system). Thus, after a brief review of probability theory, in Sect. 2, we shall commence this course, in Sect. 3, by examining how many of the central ideas of quantum mechanics are a direct consequence of wave-particle duality--i.e., the concept that waves sometimes act as particles, and particles as waves. We shall then go on to investigate the rules of quantum mechanics in a more systematic fashion in Sect. 4. Quantum mechanics is used to examine the motion of a single particle in one-dimension, many particles in one-dimension, and a single particle in three-dimensions in Sects. 5, 6, and 7, respectively. Section 8 is devoted to the investigation of orbital angular momentum, and Sect. 9 to the closely related subject of particle motion in a central potential. Finally, in Sects. 10 and 11, we shall examine spin angular momentum, and the addition of orbital and spin angular momentum, respectively.

Part II of this course consists of a description of selected applications of quantum mechanics. In Sect. 12, time-independent perturbation theory is used to investigate the Stark effect, the Zeeman effect, fine structure, and hyperfine structure, in the hydrogen atom. Time-dependent perturbation theory is employed to study radiative transitions in the hydrogen atom in Sect. 13. Section 14 illustrates the use of variational methods in quantum mechanics. Finally. Sect. 15 contains an introduction to quantum scattering theory.