Quantum Physics

PHYS30001 Quantum Physics 10 Semester 1 Undergraduate Level 3 Michael Birse Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 The unit will briefly introduce the ideas of vector spaces as used in quantum mechanics and the Dirac notation to represent quantum states. These ideas will be linked back to the wave-function approach that these students met in their second year. It will then develop operator-based approaches to the harmonic oscillator and time evolution of quantum system. The approach will then be applied to angular momentum in quantum mechanics and, in particular, to spin-1/2 systems. The interactions of these systems with magnetic fields will be explored. The rules for addition of angular momenta will be derived. Time-independent perturbation theory will be introduced and applied, at first order, to magnetic interactions of electrons in atoms. These will include the fine structure of hydrogen and the Zeeman effect. The unit will also introduce methods for handling time-dependent Hamiltonians and apply these to examples including the manipulation of spins using oscillating fields, and the basic principles of lasers.  The unit will briefly introduce the ideas of vector spaces as used in quantum mechanics and the Dirac notation to represent quantum states. These ideas will be linked back to the wave-function approach that these students met in their second year. It will then develop operator-based approaches to the harmonic oscillator and time evolution of quantum system. The approach will then be applied to angular momentum in quantum mechanics and, in particular, to spin-1/2 systems. The interactions of these systems with magnetic fields will be explored. The rules for addition of angular momenta will be derived. Time-independent perturbation theory will be introduced and applied, at first order, to magnetic interactions of electrons in atoms. These will include the fine structure of hydrogen and the Zeeman effect. The unit will also introduce methods for handling time-dependent Hamiltonians and apply these to examples including the manipulation of spins using oscillating fields, and the basic principles of lasers.  The unit aims to develop further the ideas of quantum mechanics and some of the methods needed to apply it to oscillators, angular momentum, and time-dependent systems.   On the successful completion of the course, students will be able to:  ILO 1Use Dirac notation to represent quantum-mechanical states and operatorsILO 2Work with angular momentum operators and their eigenvalues  ILO 3Calculate first-order shifts in energy levels produced by magnetic interactionsILO 4Find the time dependence of quantum states, including examples with time-dependent Hamiltonians The unit will be delivered on-line through directed reading and work on examples sheets. This will be supported by weekly in-person examples classes and office hours. The on-line materials will include: lecture notes, examples sheets, references to relevant chapters of textbooks, quizzes, and a Piazza discussion forum.  1 Written exam 100% PHYS20101 Introduction to Quantum Mechanics Pre-Requisite Compulsory N F. Mandl, Quantum Mechanics (Wiley)S. Gasiorowicz, Quantum Physics (Wiley)D. J. Griffiths, Introduction to Quantum Mechanics (Cambridge)  Lectures 11 Seminars 11 0 78