# Module Information

- Professor Pete Vukusic (Professor - Exeter University)

#### Course Delivery

#### Assessment

Assessment Type | Assessment length / details | Proportion |
---|---|---|

Semester Exam | 3 Hours Written examination | 70% |

Semester Assessment | Course work | 30% |

Supplementary Exam | 3 Hours Written examination | 100% |

### Learning Outcomes

On successful completion of this module students should be able to:

1. Present and classify the basic principles of the quantum mechanical concepts of waves, particles and wave packets.

2. Explain the limits of classical physics at the microscopic level and formulate basic physical systems in terms of Schrodinger's equation.

3. Identify and illustrate the concepts that lead to the explanation of discrete bound states, scattering and tunnelling on the smallest scales, including the fundamental ideas behind the quantum solution of the hydrogen atom.

4. Summarise the concept of spin, and its role in understanding magnetic properties of materials.

5. Analyse and solve simple numerical problems in quantum mechanics at the microscopic level.

### Aims

Quantum mechanics is a theory developed to explain inconsistencies of classical mechanics when dealing with very small objects. Its fundamental idea is that for microscopic particles (e.g. the electron) the position and momentum cannot be measured independently. Classical mechanics is fully contained in quantum mechanics as its limit for objects of larger than atomic size. However, quantum mechanics has implications for phenomena at much larger scales, e.g. energy bands in solids. Quantum-mechanical properties are the basis of techniques such as magnetic resonance imaging and scanning tunnelling microscopy.

### Brief description

This Year 2, 20-credit module develops the Quantum Physics of the microscopic world. The concept of the wavefunction is introduced together with the time-dependent and the time-independent Schroedinger Equation. Photons, electrons, protons and neutrons are described and the consequences of the Uncertainty Principle emphasised. Quantisation, scattering and tunnelling phenomena are covered in the context of the particle in a well and the simple harmonic oscillator. The quantum solution of the hydrogen atom is given and the concept of spin is extended to the understanding of magnetic properties. Throughout the module illustrative numerical problems are given relating to quantum mechanics and physically realistic examples.

### Content

Limits of classical physics: black body radiation, photo-electric effect.

Recap of wave-particle duality.

De Broglie relationships.

Wavefunction and its interpretation.

Time-dependent and time-independent Schroedinger equations.

Operators, eigenvalues, eigenvectors and possible results of a measurement.

Expectation values.

Solution of the Schroedinger equation for an infinite well.

Degeneracy. Correspondence Principle. Symmetric and anti-symmetric solution.

Zero-point energy. Heisenberg Uncertainty Principle.

Periodic potentials (Kronig-Penney model), valence and conduction bands.

Bosons and Fermions.

Scattering by a finite well.

Tunnelling. Scanning Tunnelling Microscope.

Quantum representation of angular momentum.

Hydrogen atom. Shape of wave functions.

Introduction to perturbation theory and variational principle.

Spin, directional quantisation magnetism.

Quantum entanglement.

### Module Skills

Skills Type | Skills details |
---|---|

Application of Number | Physics problems are heavily numeracy-dependent. |

Improving own Learning and Performance | Feedback from example sheets will help students improve learning. |

Problem solving | Students are required to apply theoretical concepts covered in lectures to specific science problems. |

### Notes

This module is at CQFW Level 5