Newcastle University

Aims

To introduce the wave theory of matter and other aspects of basic quantum theory.

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 introduces quantum mechanics in terms of waves and explains how to formulate and solve the Schrodinger equation for matter waves. Some basic ideas are described by considering a bouncing ball in one dimension. This is then developed into a mathematical description of a simple harmonic oscillator and a hydrogen atom. Many body theory and quantum fluids will be introduced, and then some of the more puzzling aspects of quantum mechanics and its interpretation will be discussed.

Outline Of Syllabus

Preliminary concepts: The collapse of determinism and the uncertainty principle. Schrodinger's wave theory of matter. Wave mechanics: a bouncing ball in one dimension; a simple harmonic oscillator; a hydrogen atom; many body theory and quantum fluids. The formal rules of quantum mechanics: New ideas involving operators and states will be be introduced, leading to the concepts of spin and angular momentum. Applications: Ideas on the interpretation of quantum mechanics will be introduced, which relate to quantum computers and cryptography.

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. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Written assignments (approximately 5 pieces of work of approximately equal weight) 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; this is thus formative as well as summative assessment.