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Programme & Unit Catalogues

## PH20060: Quantum & atomic physics [WL]

Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 1
Assessment: EX 85%, PR 15%
Supplementary Assessment: PH20060 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must (take PH10001 or take PH10048) and take PH10008 and in taking this unit you cannot take PH20013
Description: Aims:
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.

Learning Outcomes:
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;
* conduct short experiments on various topics, record details of experimental method and results to an appropriate standard, and write a scientific report displaying an appropriate standard of structure, attention to detail and analysis.

Skills:
Written Communication T/F A, Numeracy T/F A, Data Acquisition, Handling, and Analysis T/F A, Information Technology T/F A, Problem Solving T/F A, Working as part of a group T/F, Practical laboratory skills T/F A.

Content:
Basic assumptions of quantum mechanics (4 hours): Wave functions, 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.
Laboratory: Performance of experiments designed further to develop practical skills and support lecture material.
Programme availability:

#### PH20060 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 2
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 2
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• UXXX-AFM01 : MSci (hons) Natural Sciences (Full-time) - Year 2
• UXXX-AKM02 : MSci (hons) Natural Sciences with Professional Placement (Full-time with Thick Sandwich Placement) - Year 2
• UXXX-AAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 2
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 2
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 2

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.