Department of Physics, Unit Catalogue 2011/12
|Level:||Honours (FHEQ level 6)|
|Supplementary Assessment:||Mandatory extra work (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must (take PH20013 or take PH20060) and take PH20019 and take PH20020|
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. The unit builds on unit PH20013/60 by providing a more formal and mathematical approach to quantum mechanics.
After taking this unit the student should be able to:
* explain the relation between wave functions, operators and experimental observables;
* use wavefunction, Dirac and matrix representations of quantum mechanics;
* set up the Schrödinger equation for model systems;
* derive eigenstates of energy, momentum and angular momentum;
* apply approximate methods to more complex systems.
Numeracy T/F A, Problem Solving T/F A.
Concepts and postulates of quantum mechanics (8 hours): The wavefunction and its interpretation. Observables and operators: position, momentum, energy operators. Properties of Hermitian operators: real eigenvalues, orthogonal eigenfunctions, expansion in a complete set of eigenfunctions. Measurements of a quantum system, collapse of the wavefunction. Probabilities of measurements, expectation values. Compatible observables, commutators, the uncertainty principle. Time evolution of the wavefunction, time dependent Schrödinger equation. Stationary states, time independent Schrödinger equation. Spreading of a Gaussian wavepacket. Dirac notation. Matrix representation of quantum mechanics.
Angular momentum (4 hours): Definitions, operators and commutators. Ladder operators. Eigenvalues and eigenfunctions, spherical harmonics. Spin angular momentum, Pauli spin matrices.
Solutions of the Schrödinger equation in 3D (3 hours): Separation in Cartesian and spherical polar coordinates. Examples, including the hydrogen atom.
Approximate methods (5 hours): Stationary states: non-degenerate and degenerate perturbation theory. Examples. Time-dependent perturbation theory: Fermi's golden rule, atomic transitions, selection rules.
Identical particles (2 hours): Symmetry relations for bosons and fermions. Pauli exclusion principle.
PH30030 is Compulsory on the following programmes:Department of Physics
PH30030 is Optional on the following programmes:Programmes in Natural Sciences