Department of Physics, Unit Catalogue 2007/08 |
PH30030 Quantum mechanics |
| Credits: 6 |
| Level: Honours |
| Semester: 1 |
| Assessment: EX100 |
| Requisites: |
| Before taking this unit you must (take PH20013 or take PH20060) and take PH20019 and take PH20020 |
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Aims: The aim of this unit is to show how quantum theory can be developed from a few basic postulates and how this leads to an understanding of a wide variety of physical phenomena. To introduce the methods used to solve problems in quantum mechanics.
Learning Outcomes: After taking this unit the student should be able to: * explain the relation between wave functions, operators and experimental observables; * set up the Schrödinger equation for model systems; * derive eigenstates of energy, momentum and angular momentum; * apply approximate methods to more complex systems. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Quantum mechanical concepts and postulates (4 hours): The state of a quantum system. Hilbert space. Observables and operators. Eigenvalues and eigenfunctions. Dirac bra and ket vectors. Basis functions and representations. Probability distributions and expectation values of observables. Schrödinger equation (4 hours): Operators for position, time, momentum and energy. Derivation of time-dependent Schrödinger equation. Correspondence to classical mechanics. Commutation relations and the Uncertainty Principle. Time evolution of states. Motion of a wave packet. Stationary states and the time-independent Schrdinger equation. Review of motion in one dimension (1 hour). Motion in three dimensions (5 hours): Stationary states of free particles. Central potentials; quantisation of angular momentum. Square well; ground state of the deuteron. The hydrogen atom. Spin angular momentum (3 hours): Pauli spin matrices. Identical particles. Symmetry relations for bosons and fermions. Pauli's exclusion principle. Approximate methods for stationary states (3 hours): Non-degenerate and degenerate perturbation theory. The variational method. Scattering of particles; the Born approximation. Time-dependent perturbation theory (2 hours): Fermi's golden rule. Selection rules in atomic spectra. |