Prerequisite: MT320
Teaching: 33hr lectures
Assessment: 2hr written examination
· To derive methods, such as the Rayleigh-Ritz variational principle and perturbation theory, in order to obtain approximate solutions of the Schrödinger equation.
· To introduce spin and the Pauli exclusion principle and hence explain the mathematical basis of the Periodic table of elements.
· To introduce the quantum theory of the interaction of electromagnetic radiation with matter using time dependent perturbation theory.
· To show how scattering theory is used to probe interactions between particles and hence to show how the probability or cross section for a scattering event to occur can be derived from quantum theory.
On completion of the course students should be able to:
· use various methods to obtain approximate eigenvalues and eigenfunctions of any given Schrödinger equation,
· to understand the importance of spin in quantum theory,
· to appreciate how the Periodic Table of elements follows from quantum theory,
· to write down the Schrödinger equation for the interaction of electromagnetic radiation with the hydrogen atom and to work out photoabsorption cross sections for hydrogen,
· to define the scattering cross section and to work it out for some simple systems.
Variational principles in quantum mechanics: the Rayleigh-Ritz variational principle. Bounds on energy levels for quantum systems.
Perturbation theory: Rayleigh-Schrödinger time-independent perturbation theory. Perturbations of energy levels due to external electromagnetic fields.
The electron’s spin: the eigenfunctions and eigenvalues of the spin operator. The Pauli exclusion principle. The periodic table of elements. Spin precession in an external magnetic field.
Radiative transitions: the absorption and emission of electromagnetic radiation by matter. Photoabsorption cross-sections for the hydrogen atom.
Scattering theory: definition of the scattering cross-section and the scattering amplitude. Decomposition of the scattering amplitude into partial waves. Phase shifts and the S-matrix. Integral representations of the scattering amplitude. The Born approximation. Potential scattering.
Quantum Physics –
Quantum Mechanics – P C W Davies (Chapman and Hall 1984)
Library reference 530.12 DAV