# MMath&Phys Mathematics and Physics / Course details

Year of entry: 2024

## Course unit details:Quantum Physics and Relativity

Unit code PHYS10121 10 Level 1 Semester 1 No

### Overview

Quantum Physics and Relativity

### Aims

1. To explain the need for and introduce the principles of the Special Theory of Relativity.
2. To develop the ability to use the Special Theory of Relativity to solve a variety of problems in relativistic kinematics and dynamics.
3. To explain the need for a Quantum Theory and to introduce the basic ideas of the theory.
4. to develop the ability to apply simple ideas in quantum theory to solve a variety of physical problems.

### Learning outcomes

On completion successful students will be able to:

1. define the notion of an inertial frame and the concept of an observer.
2. state the principles of Special Relativity and use them to derive time dilation and length contraction.
3. perform calculations using the Lorentz transformation formulae
4. define relativistic energy and momentum, and use these to solve problems in mechanics.
5. perform calculations using four-vectors.
6. use the ideas of wave-particle duality and the uncertainty princple to solve problems in quantum mechanics.
7. perform calculations using the quantum wave- function of a particle moving in one dimension, including making use of the momentum operator.
8. use the Bohr formula to calculate energies and wavelengths in the context of atomic hydrogen.

### Syllabus

Relativity

• Galilean relativity, inertial frames and the concept of an observer.
• The principles of Einstein’s Special Theory of Relativity
• Lorentz transformations: time dilation and length contraction.
• Velocity transformations and the Doppler effect.
• Spacetime and four-vectors.
• Energy and momentum with applications in particle and nuclear physics.

Quantum Physics

• Basic properties of atoms and molecules. Atomic units. Avogadro’s number.
• The wavefunction and the role of probability.
• Heisenberg’s Uncertainty Principle and the de Broglie relation.
• The momentum operator and the time-independent Schrödinger equation: the infinite square well.
• Applications in atomic, nuclear and particle physics: energy levels spectra and lifetimes.

Method Weight
Other 10%
Written exam 90%

### Feedback methods

Feedback will be offered by tutors on students’ written solutions to weekly examples sheets, and model answers will be issued.

Recommended text

Forshaw, J.R. & Smith, G, Dynamics & Relativity (John Wiley & Sons)

Young, H.D. & Freedman, R.A., University Physics (Addison-Wesley)

Supplementary texts:

Cox, B.E. & Forshaw, J.R. Why does E=mc²? (and why should we care?) (Da Capo)

Cox, B.E. & Forshaw, J.R. The Quantum Universe (Allen Lane)

Rindler, W. Relativity: Special, General & Cosmological (Oxford)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Tutorials 6
Independent study hours
Independent study 70.5

### Teaching staff

Staff member Role
Jeffrey Forshaw Unit coordinator
Brian Cox Unit coordinator