# QUANTUM MECHANICS - 2024/5

Module code: MAT3039

## Module Overview

This module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin.

This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.

### Module provider

Mathematics & Physics

### Module Leader

TORRIELLI Alessandro (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 6

### Module cap (Maximum number of students): N/A

## Overall student workload

Independent Learning Hours: 69

Lecture Hours: 33

Guided Learning: 15

Captured Content: 33

## Module Availability

Semester 2

## Prerequisites / Co-requisites

You cannot also take PHY3044 ADVANCED QUANTUM PHYSICS.

## Module content

Indicative content includes:

- Crucial experiments and birth of quantum mechanics.
- Hilbert spaces and Dirac notation.
- Postulates of Quantum Mechanics. The uncertainty principle. Wave functions.
- The Hamiltonian operator and its spectrum. The Schroedinger equation. Observables.
- Applications: Particle in a one-dimensional potential well. The tunneling effect. The one-dimensional quantum harmonic oscillator.
- Advanced topics: Angular momentum and its addition rules. Spin. The Pauli exclusion principle.
- Advanced applications (time-permitting): The Hydrogen Atom. Time-independent perturbation theory and energy level-splitting.

## Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

School-timetabled exam/test | In-semester test (50 min) | 20 |

Examination | End-of-Semester Examination (2 hours) | 80 |

## Alternative Assessment

N/A

## Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate:

- Understanding of subject knowledge, and recall of key postulates and theorems in Quantum Mechanics.
- The ability to analyse unseen problems in Quantum Mechanics, and use appropriate methods to solve these problems and interpret the results.

Thus, the

__summative assessment__for this module consists of:

- One in-semester test corresponding to Learning Outcomes 1, 2 and 5.
- A synoptic examination corresponding to all Learning Outcomes 1 to 5.

Formative assessment

There are two formative unassessed courseworks over an eleven week period, designed to consolidate student learning.

Feedback

Students will receive individual written feedback on both the formative unassessed courseworks and the in-semester test. The feedback is timed such that feedback from the first coursework will assist students with preparation for the in-semester test. The feedback from both courseworks and the in-semester test will assist students with preparation for the synoptic examination. Students also receive verbal feedback in office hours.

## Module aims

- Introduce students to the mathematical description of quantum phenomena.
- Enable students to understand the postulates of Quantum Mechanics and their applications to the physical world.
- Illustrate the application of the theory of Quantum Mechanics to simple one-dimensional examples, including a particle in a potential well, the quantum harmonic oscillator and spin systems.

## Learning outcomes

Attributes Developed | ||

001 | Students will demonstrate a firm understanding of the concepts, theorems and mathematical techniques underlying Quantum Mechanics. | KC |

002 | Students will be able to solve the Schroedinger equation for examples involving one-dimensional potential wells and quantum tunnelling. | KC |

003 | Students will be able to apply mathematical techniques to solve the quantum harmonic oscillator. | KC |

004 | Students will be able to apply mathematical techniques to quantum systems involving angular momentum and spin. | KC |

005 | Students will be able to analyse, solve and interpret unseen problems in Quantum Mechanics similar to those encountered in the module. | KCT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to:

- Introduce students to the postulates and theory of Quantum Mechanics, and appropriate mathematical tools for their implementation.
- Provide students with experience of methods used to interpret, understand and solve concrete problems in Quantum Mechanics.

The learning and teaching methods include:

- Three one-hour lectures for eleven weeks, with module notes provided to complement the lectures. These lectures provide a structured learning environment and opportunities for students to ask questions and to practice methods taught.
- Two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive feedback on these courseworks as guidance on their progress and understanding.
- Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students an opportunity to review parts of lectures which they may not fully have understood and should not be seen as an alternative to attending lectures.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **MAT3039**

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

**Digital Capabilities:** The SurreyLearn page for MAT3039 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

**Employability: **The module MAT3039 equips students with skills which significantly enhance their employability. The mathematical proficiency gained will hone their critical thinking and problem-solving abilities. Students will learn to interpret and evaluate quantum problems, model these problems mathematically using the tools of Quantum Mechanics, and hence deduce and interpret solutions. Mathematical modeling is a highly sought after skill in many professions.

**Global and Cultural Capabilities:** Students enrolled in MAT3039 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in lectures, which naturally facilitates the sharing of different cultures.

**Resourcefulness and Resilience:** MAT3039 is a module which demands the ability to analyse complex problems in Quantum Mechanics, formulate and solve these problems mathematically using mathematical tools and quantum theory, and interpret the results. Students will gain skills in analysing unseen problems and lateral thinking, and will complete assessments which challenge them and build resilience.

**Sustainability:** Quantum Mechanics can be used to model physical systems relevant to sustainable practices. For instance, Quantum Mechanics can be used to model energy levels in atoms and nuclei, energy level transitions and the resulting release of energy. This is the mechanism behind nuclear reactions which produce nuclear energy. One or more case studies will be included in the module relating to applications of Quantum Mechanics to quantum systems relevant to real-world sustainable practices.

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics with Statistics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Statistics MMath | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Music BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Financial Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MPhys | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MMath | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Economics and Mathematics BSc (Hons) | 2 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.