# PX101 Quantum Phenomena

## Weighting: 6 CATS

This module begins by showing how classical physics is unable to explain some of 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 some of the key 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.

Aims:
To describe how the discovery of effects which could not be explained using classical physics led to the development of quantum theory. The module should develop the ideas of wave-particle duality and introduce the wave theory of matter based on Schrödinger's equation.

Objectives:
At the end of the module you should be able to:

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

Syllabus:

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.

Commitment: 15 Lectures + 5 problems classes

Assessment: 1 hour examination

Recommended Texts: H D Young and R A Freedman, University Physics, Pearson.

This module has a home page with links to various documents and biographies.

Leads from: A-level Physics and Mathematics