# QUANTUM PHYSICS - 2024/5

Module code: PHY2069

## Module Overview

The Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.

### Module provider

Mathematics & Physics

### Module Leader

FAUX David (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 5

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

## Overall student workload

Independent Learning Hours: 63

Lecture Hours: 33

Tutorial Hours: 11

Guided Learning: 10

Captured Content: 33

## Module Availability

Semester 1

## Prerequisites / Co-requisites

None.

## Module content

Indicative content includes:

**1. ****Origins of quantum mechanics**

Brief review of the old quantum theory (pre-1925): the Planck formula, Einstein’s contribution and the De Broglie wavelength

**2.**

**The “Wave Function” and the Schrödinger equation**

The wave function (or probability amplitude); postulates of quantum mechanics; probability density functions – the |Ψ|2; the free particle

**3.**

**Operators**

General definition of an operator; operators in the Schrödinger equation; the momentum operator; eigenvalues and eigenfunctions of an operator; the Hamiltonian and other operators; introduction to matrix operators; eigenvalues and eigenfunctions of the position operator; expectation values

**4.**

**Wave Packets**

Introduction to wave packets; the Heisenberg Uncertainty Principle

**5. Solving the time-dependent Schrödinger equation**

- The method for finding solutions to the time-dependent wave function.

**6. Solving the Schrödinger equation in 1D**

The infinite square well potential (particle in a box) stationary and bound states; the harmonic oscillator potential.

**7. The Step Potential**

The step potential in 1-D; reflection and transmission coefficients; the potential barrier and quantum tunnelling.

**8. Superposition, Completeness and Orthogonality**

Superposition and completeness; non-locality. Orthogonality. Derivation and normalisation of the expansion coefficients; physical interpretation of expansion coefficients.

**9. Commutating and compatible observables**

Commutation relations and their relevance to quantum physics; Heisenberg’s Uncertainty Principle revisited.

**10. Perturbation**

- The first-order time-independent perturbation and its use in quantum mechanics

## Assessment pattern

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

Coursework | COURSEWORK ASSIGNMENT 1 | 20 |

Coursework | COURSEWORK ASSIGNMENT 2 | 20 |

Examination | END-OF-SEMESTER EXAMINATION - 2 hours | 60 |

## Alternative Assessment

N/A

## Assessment Strategy

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

- recall of subject knowledge
- ability to apply subject knowledge to unseen problems

Thus, the

__summative assessment__for this module consists of :

- two homework assignments
- a 2.0 hour invigilated examination at the end of the semester, with a section A of compulsory questions and a section B with 2 questions chosen from 3. In Part A answer all questions (30 points); In Part B answer two questions out of three (15-points each).

__Formative assessment and feedback__

Students receive feedback (marks, comments) during weekly tutorials, which are online, when they wish. Verbal help and advice is given in tutorials. The full solutions are issued on SurreyLearn on a weekly basis.

## Module aims

- Introduce the concept of a complex probability amplitude and to explore its role in making physical predictions.
- introduce the Schrödinger equation in quantum physics.
- develop the properties of a linear operator, its eigenvalue spectrum and properties of its eigenfunctions.
- provide methods to calculate bound state eigenfunctions in an infinite square well potential.
- explore one-dimensional quantum systems and their applications
- introduce concepts such as superposition, orthogonality and completeness.
- develop proficiency in the application of mathematical methods to these problems.

## Learning outcomes

Attributes Developed | ||

001 | Describe the role of the wave function in quantum mechanics | K |

002 | Calculate probability densities, probabilities, means and uncertainties (standard deviations) | C |

003 | Solve homogeneous and inhomogeneous ordinary second order differential equations: | C |

004 | Use operators, operator expressions and commutators; | C |

005 | Find eigenvalues and eigenvectors of common operators; | C |

006 | Use the relation between eigensolutions and results of measurements | C |

007 | Understand and interpret the Heisenberg's Uncertainty Principle | KC |

008 | Calculate and interpret eigensolutions of an infinite square well | C |

009 | To understand and interpret solutions for the parabolic potential well | C |

010 | Use superpositions of energy eigenstates, to find their time evolution and interpret their probability densities | C |

011 | Solve Schrödinger's equation for step and barrier potentials; to find transmission and reflection coefficients and to compare quantum and classical results | C |

012 | Calculate, interpret and use eigenfunction expansions | C |

013 | Apply the first-order, time-independent perturbation expression and to calculate first-order energy corrections | C |

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:

- equip students with subject knowledge
- develop skills in applying subject knowledge to physical situations
- enable students to tackle unseen problems in mathematics and quantum physics

The

__learning and teaching__methods include:

- Lectures and Computer-based Tutorials

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: **PHY2069**

## Other information

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

**Digital Capabilities **

Quantum physics is fundamentally digital with physical quantities restricted to certain discrete values. Quantum computing is just one emerging digital technology that exploits quantum mechanics to perform complex computations more efficiently. The quantum physics module teaches the foundational principles that underpin quantum computing.

**Employability**

Quantum physics aids the development of a range of skills that are highly valued in the job market, such as problem-solving, critical thinking, and analytical reasoning. There is a growing demand for skilled professionals who can develop and implement the emerging technologies underpinned by quantum mechanics and which are expected to revolutionize fields such as computing, communications, and sensing over the next decades.

**Global and Cultural Capabilities**

Historically, the development of quantum technologies has revolutionized many industries, from computing to communications, from energy to healthcare. By studying quantum physics, students are gaining the background knowledge and skills underpinning emerging new technologies that can benefit people all over the world, such as quantum computing, quantum encryption and quantum biology.

**Resourcefulness and Resilience **

Quantum physics is a field that requires a high degree of resourcefulness as it involves working with abstract concepts and solving difficult mathematical problems. Resourcefulness and resilience are developed through the formative weekly online tutorials with hints that allow students to try and re-try problem parts to develop their understanding of the discipline. Students also develop their problem-solving skills through challenging take-home assignments.

**Sustainability**

Renewable energy: solar cells and quantum dots are key components in photovoltaic devices that rely on principles of quantum physics. Materials: our own research seeking to reduce the carbon footprint of the cement production cycle (currently third largest CO2 contributor) requires quantum mechanical simulation techniques to understand the carbonation process. Environmental monitoring: quantum physics contributes to sustainability by enabling more precise and accurate environmental monitoring through quantum sensors that can detect and measure pollutants in air and water with greater sensitivity and specificity than traditional methods.

## Programmes this module appears in

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

Physics with Astronomy BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Physics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Physics with Nuclear Astrophysics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Physics with Nuclear Astrophysics MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Physics with Astronomy MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Physics MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Physics with Quantum Computing BSc (Hons) | 1 | Optional | A weighted aggregate mark of 40% is required to pass the module |

Physics with Quantum Computing MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MMath | 1 | Compulsory | 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.