## PHYS2311 Physics 4- Quantum Phenomena

### 25 creditsClass Size: 250

Module manager: Dr Zlatko Papic
Email: Z.Papic@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2023/24

### This module is mutually exclusive with

 PHYS2360 Quantum Mechanics (Joint Honours)

This module is not approved as a discovery module

### Objectives

By the end of the module you should be able to:

Quantum Mechanics:
- write down the time dependent and time independent Schrodinger Equations;
- recall the form of and properties of wave functions, eigenfunctions and probability functions;
- derive the form of the wavefunction for a particle confined in an infinite square well;
- recall the form of the wavefunctions for other confining potentials;
- understand and use the Heisenberg Uncertainty Principle;
- use operators to calculate expectation values;
- describe the concepts of symmetrical and antisymmetrical wave functions;
- explain in general terms the Pauli Exclusion Principle and use spin functions;
- describe the quantum mechanical model of the hydrogen atom;
- describe the electron configuration of atoms and their spectra;
- describe the quantum mechanical origins of ionic and covalent bonds.
- describe the principle of laser action

Nuclear and Particle Physics:
-discuss components of the Standard Model of Particle Physics
-understand and interpret Feynman diagrams
-discuss different models of the nucleus
-estimate nuclear masses
-discuss and predict various forms of radioactive decay and nuclear reactions

Condensed Matter:
- use the density of states to explain some of the differences between metals, semiconductors and insulators;
- derive the free-electron density of states;
- perform straight-forward calculations based on the free-electron theory;
- explain how a periodic potential modifies the free-electron dispersion relation;
- solve problems on the transport properties of semiconductors;
- calculate the magnetic properties (consistent with the syllabus) of paramagnets and ferromagnets.

Learning outcomes
Students will be able to demonstrate knowledge, understanding and application of the following:

In Quantum Mechanics:
(1) Probabilistic description of quantum systems using wave functions and the Schroedinger equation;
(2) Predicting outcomes of measurements on quantum systems using operators, observable expectation values and the Heisenberg uncertainty principle;
(3) Describe the behaviour of a quantum particle in one-dimensional potentials, including the potential well, harmonic oscillator potential, propagation across potential barriers and quantum tunnelling;
(4) Quantum-mechanical model of the hydrogen atom;
(5) Pauli exclusion principle, spin and electronic structure of atoms;
(6) Quantum-mechanical origin of chemical bonds and the principle of laser action.

In Nuclear and Particle Physics:
(1) Main components of the Standard Model of Particle Physics;
(2) Understanding and interpretation of Feynman diagrams;
(3) Different models of the atomic nucleus and estimating nuclear masses;
(4) Predicting various forms of radioactive decay and nuclear reactions.

In Condensed Matter:
(1) Using the density of states to explain some of the differences between metals, semiconductors and insulators;
(2) Describing properties of solids using free-electron theory;
(3) The effect of periodic potential on the free-electron dispersion relation;
(4) Transport properties of semiconductors;
(5) Magnetic properties of paramagnets and ferromagnets.

Skills outcomes
Understanding of core Quantum Mechanics, Solid State Physics and Particle Physics

### Syllabus

Quantum Mechanics
-Schrodinger equation,
-wave function,
-standard solutions,
-Hydrogen atom,
-spin,
-Pauli exclusion principle,
-Fermions and Bosons.
-1st order time independent perturbation theory, periodic table, quantum structure, spectra of simple atoms, laser action.

Condensed Matter:
-free electron model;
-phonons;
-electrons in a periodic potential
-semiconductors;
-magnetic properties of solids.

Nuclear and Particle Physics:
-introduction to particle physics
-Feynman diagrams
-models of the nucleus
-nuclear reactions

### Teaching methods

 Delivery type Number Length hours Student hours Office Hour Discussions 11 1.00 0.00 Lecture 66 1.00 66.00 Independent online learning hours 55.00 Private study hours 129.00 Total Contact hours 66.00 Total hours (100hr per 10 credits) 250.00

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Regular coursework 20.00 Total percentage (Assessment Coursework) 20.00

Resit will be in standard exam format.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound.