Quantum Control group

PHYS 2023 Wave Physics   Unit Coordinator: Dr Tim Freegarde Semester: 1   Prerequisites: First year physics core units Credit Points: 15   This is a core unit for all physics programmes

Introduction

This course introduces the properties and mechanics of waves, from the derivation and solution of wave equations, through the origins of the classical processes of refraction, dispersion and interference, to the quantum mechanical phenomenon of the uncertainty principle. It will arm students with a basic knowledge of wave behaviour and propagation, together with techniques for their quantitative analysis and application to a range of physical systems. It will further provide a fundamental base from which to examine wave aspects of electromagnetism, quantum mechanics and solid state physics in subsequent courses.

Learning Outcomes

After studying this course, students should have a basic knowledge and understanding of:

• the nature of wave propagation and its physical mechanisms
• the derivation and solution of wave equations, both in general and for specific systems
• travelling, standing and harmonic wave solutions
• interference and the Huygens model of wave propagation; reflection, refraction and diffraction
• superpositions, wave packets and Fourier analysis
• dispersion and the phase and group velocities
• the physical basis of continuity conditions and their implications for interfaces
• the energy and momenta of wave motions
• wave mechanical operators and the average properties of superpositions

Syllabus

1. general principles of wave propagation; derivation and solution of wave equations
2. transverse waves; travelling, standing and harmonic solutions; initial conditions
3. linearity, interference, superposition and the Huygens construction for wave propagation
4. Fourier series and transforms; the convolution theorem
5. wave packets, dispersion and phase and group velocities
6. diffraction: single slit, double slit, grating and general Fraunhofer results
7. multiple-path interference and interferometers
8. energy and momentum transport in wave motions
9. continuity conditions and interfaces
10. longitudinal waves; waves from moving sources; waves in various physical systems
11. wave mechanical operators; wavefunction averages; transform limits and uncertainty

Teaching and Learning Methods

Teaching is through a course of 30 lectures, supplemented by exercises which are addressed in separate tutorial classes.

Non-contact Hours

Students are expected to pursue six hours of independent study per week.

Assessment Methods

Assessment is by written examination at the end of the course. Section A of the paper will comprise five short, compulsory questions; section B will contain four longer questions, of which only two should be answered.

Recommended Books and Course Materials

• T. Freegarde- Introduction to the Physics of Waves, Cambridge University Press(2012) ISBN 978 0521 147163
• H. J. Pain - The Physics of Vibrations and Waves, 6th edition, Wiley, Chichester (1998) ISBN 0 470 01296 X
• A. P. French - Vibrations and Waves, various publishers:
  • Chapman and Hall, London ISBN 0 442 30784 5
  • W W Norton, New York ISBN 978 0 393 09936 2
  • Nelson Thornes, Cheltenham (1971) ISBN 978 0 748 74447 3
• I. G. Main - Vibrations and Waves in Physics, 3rd edition, C U P, Cambridge (1993) ISBN 0 978 521 44701 0
• E. Hecht - Optics, 4th ed., Addison-Wesley (2001) ISBN 0 8053 8566 5
• M. L. Boas - Mathematical Methods in the Physical Sciences, Wiley, New York (1983) ISBN 978 0 471 19826 0
• R. P. Feynman- Lectures in Physics, vol. 1, Basic Books (revised 2011) ISBN 978 0 465 02493 3

Other Course Information

Skills Development

Importance on a scale of 0 (low) to 5 (high):