# QUANTUM PHYSICS - 2017/8

Module code: PHY2069

Module provider

Physics

Module Leader

FAUX DA Dr (Physics)

Number of Credits

15

ECT Credits

7.5

Framework

FHEQ Level 5

JACs code

F342

Module cap (Maximum number of students)

N/A

Module Availability

Semester 1

Overall student workload

Independent Study Hours: 106

Lecture Hours: 33

Assessment pattern

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

Coursework | COURSEWORK ASSIGNMENT | 30% |

Examination | END OF SEMESTER 1.5HR EXAMINATION | 70% |

Alternative Assessment

None

Prerequisites / Co-requisites

None.

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 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 | |
---|---|

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

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

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

Use operators, operator expressions and commutators; | C |

Find eigenvalues and eigenvectors of common operators; | C |

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

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

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

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

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

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

Calculate, interpret and use eigenfunction expansions | C |

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

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

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

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.

Reading list

Reading list for QUANTUM PHYSICS : http://aspire.surrey.ac.uk/modules/phy2069

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 2017/8 academic year.