# QUANTUM PHYSICS - 2018/9

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

Physics

Module Leader

FAUX David (Physics)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 5

JACs code: F342

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

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.**

**Differential equations**

Homogeneous and inhomogeneous ordinary second-order differential equations; arbitrary constants of solution and boundary conditions; the solution of equations with constant coefficients; the complementary function, the particular integral; the general solution, development of the operator technique of solution, the characteristic equation, detailed solution of second order equations with constant coefficients

**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 | 30 |

Examination | END OF SEMESTER 1.5HR EXAMINATION | 70 |

Alternative Assessment

None

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 :

- one homework assignments due in week
- a final examination of 1.5h with 2 questions out of 3 to be answered

__Formative assessment and feedback__

Verbal feedback is given in tutorials. Written feedback is given on the first assignment to inform the subsequent assessmnets. One piece of course work will be formatively assessed prior to the summative coursework listed above.

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

Overall student workload

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:

- 33h of lectures and 11h of computer-based tutorials as 4h/week over 11 weeks

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.

Programmes this module appears in

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

Physics with Nuclear Astrophysics MPhys | 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 Astronomy 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 BSc (Hons) | 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 |

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

Liberal Arts and Sciences BA (Hons)/BSc (Hons) | 1 | Optional | 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 Astronomy MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

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

Physics with Quantum Technologies BSc (Hons) | 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 2018/9 academic year.