|Owning Department/School:||Department of Physics|
|Level:||Intermediate (FHEQ level 5)|
|Supplementary Assessment:||PH20013 - Mandatory Extra Work (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must (take PH10001 or take PH10048) and (take PH10005 or take PH10053) and take PH10007 and take PH10008)|
The aims of this unit are to introduce the Schrödinger equation and its solution in one and three dimensions, and to discuss the interactions responsible for the electronic structure of atoms.
After taking this unit the student should be able to:
* explain the significance of the wavefunction in determining the physical behaviour of electrons;
* show how quantisation arises from boundary conditions and calculate energy levels in simple model systems;
* discuss the energy levels, angular momenta and spectra of atoms, taking into account screening, magnetic interactions and the exchange interaction.
Numeracy T/F A, Problem Solving T/F A.
Basic assumptions of quantum mechanics (4 hours): Wave function, probability density and normalisation. Observables; position, momentum and energy. Schrödinger's equation; time dependence of the wavefunction, stationary states, time-independent Schrödinger equation.
Motion in one dimension (6 hours): States of the infinite square well, parity of solutions, bound states of the finite square well. Motion of free particles. Reflection and transmission at a step. Tunnelling through a barrier. The harmonic oscillator.
Motion in three dimensions (9 hours): The hydrogen atom. Angular dependence of solutions, spherical harmonics, s,p,d states. Radial solutions, radial probability distribution functions, energy levels. Orbital and spin angular momentum and their associated magnetic moments. Spin-orbit coupling. Zeeman effect. Atomic spectra; selection rules, width of spectral lines, laser cooling of atoms.
Many-electron atoms (3 hours): Pauli exclusion principle and shell structure. Electron-electron interactions; screening and exchange interaction. Nomenclature for labelling atomic configurations and terms. Hund's rules. Spectra of many-electron atoms.
PH20013 is Compulsory on the following programmes:Department of Physics
PH20013 is Optional on the following programmes:Department of Mathematical Sciences