Introductory description

This module starts by explaining how classical physics is unable to explain the properties of light, electrons and atoms. (Theories in physics, which make no reference to quantum theory, are usually called classical theories.) It then deals with the most important contributions to the development of quantum physics including those of: Planck, who first suggested that the energy in a light wave comes in discrete units or 'quanta'; Einstein, whose theory of the photoelectric effect implied a 'duality' between particles and waves; Bohr, who suggested a theory of the atom that assumed that not only energy but also angular momentum was quantised; and Schrödinger who wrote down the first wave-equations to describe matter.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Waves, particles and thermodynamics before quantum theory

Light:
Thermal radiation and the origin of Quantum Theory: Blackbody Radiation, derivation for the case of a `1D black-body', the idea of modes, Wien's law, Rayleigh-Jeans formula, Planck's hypothesis and E=hf . The photoelectric effect - Einstein's interpretation.

Waves or Particles? Interference a problem for the particle picture; the Compton effect - direct evidence for the particle nature of radiation.

Matter:
Atoms and atomic spectra a problem for classical mechanics. Bohr's Model of the Atom: quantization of angular momentum, atomic levels in hydrogen. De Broglie's hypothesis. Experimental verification of wave-like nature of electrons - electron diffraction

Quantum Mechanics:
Correspondence Principle. The Schrödinger wave equation. Relation of the wavefunction to probability density. Probability distribution, need for normalization. Superpositions of waves to give standing waves, beats and wavepackets. Gaussian wavepacket. Use of wavepackets to represent localized particles. Group velocity and correspondence principle again. Wave-particle duality, Heisenberg's uncertainty principle and its use to make order of magnitude estimates.

Using Schrödinger's equation:
Including the effect of a potential. Importance of stationary states and time-independent Schrödinger equation. Infinite potential well and energy quantization. The potential step - notion of tunnelling. Alpha decay of nuclei. Status of wave mechanics.

Learning outcomes

By the end of the module, students should be able to:

• Discuss how key pieces of experimental evidence implied a wave-particle duality for both light and matter
• Discuss the background to and issues surrounding Schrödinger's equation. This includes the interpretation of the wave function and the role of wave packets and stationary states
• Manipulate the time-independent Schrödinger equation for simple 1-dimensional potentials

Indicative reading list

H. D. Yo.ung and R A Freedman, University Physics, Pearson

View reading list on Talis Aspire

Interdisciplinary

Quantum theory has been a joint endeavour between mathematics and physics since its inception. It has applications to chemistry and increasingly computer science (quantum computing). One of the founders of the subject, Dirac, was a great interdisciplinarian. He trained as an engineer and is celebrated both for his contributions to mathematics and to physics. This module is taken by many students from within Mathematical Sciences (mainly Mathematics and Physics).

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.

Transferable skills

Analytical, communication, problem-solving, self-study