Summary and Info
Quantum mechanics underpins a variety of broad subject areas within physicsand the physical sciences from high energy particle physics, solid state andatomic physics through to chemistry. As such, the subject resides at the coreof every physics programme. In the following, we list an approximate “lecture by lecture” synopsis ofthe different topics treated in this course. 1 Foundations of quantum physics: Overview of course structure andorganization; brief revision of historical background: from wave mechan-ics to the Schr¨odinger equation.2 Quantum mechanics in one dimension: Wave mechanics of un-bound particles; potential step; potential barrier and quantum tunnel-ing; bound states; rectangular well; !-function potential well; Kronig-Penney model of a crystal.3 Operator methods in quantum mechanics: Operator methods;uncertainty principle for non-commuting operators; Ehrenfest theoremand the time-dependence of operators; symmetry in quantum mechan-ics; Heisenberg representation; postulates of quantum theory; quantumharmonic oscillator.4 Quantum mechanics in more than one dimension: Rigid diatomicmolecule; angular momentum; commutation relations; raising and low-ering operators; representation of angular momentum states.5 Quantum mechanics in more than one dimension: Central po-tential; atomic hydrogen; radial wavefunction.6 Motion of charged particle in an electromagnetic ﬁeld: Classicalmechanics of a particle in a ﬁeld; quantum mechanics of particle in aﬁeld; atomic hydrogen – normal Zeeman effect; diamagnetic hydrogen and quantum chaos; gauge invariance and the Aharonov-Bohm effect; free electrons in a magnetic ﬁeld – Landau levels.7-8 Quantum mechanical spin: History and the Stern-Gerlach experi-ment; spinors, spin operators and Pauli matrices; relating the spinor tospin direction; spin precession in a magnetic ﬁeld; parametric resonance;addition of angular momenta.9 Time-independent perturbation theory: Perturbation series; ﬁrst and second order expansion; degenerate perturbation theory; Stark effect; nearly free electron model.10 Variational and WKB method: Ground state energy and eigenfunc tions; application to helium; excited states; Wentzel-Kramers-Brillouin method.11 Identical particles: Particle indistinguishability and quantum statis-tics; space and spin wavefunctions; consequences of particle statistics;ideal quantum gases; degeneracy pressure in neutron stars; Bose-Einsteincondensation in ultracold atomic gases.12-13 Atomic structure: Relativistic corrections; spin-orbit coupling; Dar-win structure; Lamb shift; hyperﬁne structure; Multi-electron atoms;Helium; Hartree approximation and beyond; Hund’s rule; periodic ta-ble; coupling schemes LS and jj; atomic spectra; Zeeman effect.14-15 Molecular structure: Born-Oppenheimer approximation; H2+ ion; H2molecule; ionic and covalent bonding; molecular spectra; rotation; nu-clear statistics; vibrational transitions.16 Field theory of atomic chain: From particles to ﬁelds: classical ﬁeldtheory of the harmonic atomic chain; quantization of the atomic chain;phonons.17 Quantum electrodynamics: Classical theory of the electromagneticﬁeld; theory of waveguide; quantization of the electromagnetic ﬁeld andphotons.18 Time-independent perturbation theory: Time-evolution operator;Rabi oscillations in two level systems; time-dependent potentials – gen-eral formalism; perturbation theory; sudden approximation; harmonicperturbations and Fermi’s Golden rule; second order transitions.19 Radiative transitions: Light-matter interaction; spontaneous emis-sion; absorption and stimulated emission; Einstein’s A and B coefficents;dipole approximation; selection rules; lasers.20-21 Scattering theory I: Basics; elastic and inelastic scattering; methodof particle waves; Born approximation; scattering of identical particles.22-24 Relativistic quantum mechanics: History; Klein-Gordon equation;Dirac equation; relativistic covariance and spin; free relativistic particlesand the Klein paradox; antiparticles and the positron; Coupling to EMﬁeld: gauge invariance, minimal coupling and the connection to non- relativistic quantum mechanics; ﬁeld quantization.