Aims

To discuss mathematically the wave theory of matter by analysing the Schrodinger equation.

Module Summary

Quantum mechanics is the theoretical framework used to describe the most fundamental properties of matter. It has a rich mathematical structure and it has provided the impetus for many advances in mathematics. It also has many practical applications, including the modelling of atoms, molecules and semiconductors. Recently, quantum theory has been used extensively to model superfluids and supercooled gases, and there are even attempts to build computers which function by the laws of quantum mechanics.

This module discusses the wave formulation of quantum mechanics in the context of the one- dimensional Schrodinger equation: this is mathematically solved in various trapped problems, including finite and infinite box and quadratic potentials, with examples including open-boundary cases.

Outline Of Syllabus

Reminder of Preliminary concepts: de Broglie and Planck relations and the uncertainty principle; brief introduction to distribution functions. Schrodinger's equation and its solutions in an infinite- and finite- height box and in a harmonic oscillator potential; simple extensions to more general potentials and quantum-mechanical tunnelling; the correspondence principle and superposition states. Open boundary problems, reflection and transmission coefficients.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work.

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.