# Module Information

#### Course Delivery

Delivery Type | Delivery length / details |
---|---|

Lecture | 32 x 1-hour lectures |

Seminars / Tutorials | 8 hours workshops |

Workload Breakdown | (Every 10 credits carries a notional student workload of 100 hours). Lectures 32 hours, Example sheets 20 hours, Private study 140 hours. |

#### 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. Describe 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 the concepts that lead to the explanation of discrete bound states, scattering and tunneling on the smallest scales, including the fundamental ideas behind the quantum solution of the hydrogen atom.

4. Appreciate the concept of spin in understanding magnetic properties of materials.

5. 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 energy is not a continuous quantity but comes in small packets ("quanta") of uniform size. 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

Building on the Year 1 models "The Quantum Universe" this Year 2, 20-credit module develops the Quantum Physics of the microscopic world. The mathematical equivalence and physical distinction between the Wave Equation and Schrodinger's Equation are emphasised at the macroscopic and quantum level. Photons, electrons and neutrons are described and the consequences of the Uncertainty Principle emphasised. Quantisation, scattering and tunneling 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 wave-particles.

### Content

Recap of wave-particle duality.

De Broglie relationships and Schrodinger's Equation.

Operators, dynamical variables and possible results of a measurement. Expectation values.

Solution of Schrodinger's equation for an infinite well.

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

Zero-point energy and specific heat at low temperatures. Uncertainty Principle.

Potential well with ion lattice. Symmetry argument for valence and conduction bands. Insulators, conductors and semi-conductors.

Bosons and Fermions. Atoms, molecules and solids

Scattering by a finite well.

Barrier penetration (approximate solution). Field-emission microscope and scanning microscope.

Quantum representation of angular momentum.

Hydrogen atom. Shape of wave functions.

Introduction to perturbation and variation theory.

Spin, directional quantisation magnetism and NMR.

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. |

### Reading List

**Essential Reading**

Phillips, A. C. (c2003.) Introduction to quantum mechanics /A.C. Phillips. Wiley Primo search

**Recommended Text**

Jewett, John W. (c2010.) Physics for scientists and engineers with modern physics. /John W. Jewett, Raymond A. Serway, with contributions from Vah e Peroomian. 8th ed., International ed. Brooks/Cole Cengage Learning Primo search

**Supplementary Text**

(2007) The quantum world.edited by John Bolton and Ray Mackintosh. Open University Primo search (2007) The quantum world.edited by John Bolton and Robert Lambourne. Open University Primo search (2007) The quantum world.edited by John Bolton and Stuart Freake. Open University Primo search Davies, P. C. W. (1984.) Quantum mechanics /P.C.W. Davies. Routledge &amp; K. Paul Primo search Feynman, Richard Phillips. (1965.) The Feynman lectures on physics /by Richard P.Feynman, Robert B. Leighton, Matthew Sands. Addison-Wesley Primo search Messiah, Albert. (1961-62.) Quantum mechanics /[Translated from the French by G.M. Temmer]. North-Holland Pub. Co Primo search Peleg, Yoav. (c1998.) Schaum's outline of theory and problems of quantum mechanics /Yoav Peleg, Reuven Pnini, Elyahu Zaarur. McGraw-Hill Primo search

### Notes

This module is at CQFW Level 5