Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

To present the formal structure of quantum mechanics, including encapsulating material at previous stages in a number of operator postulates.

To develop a number of approximation methods in quantum mechanics including the variational principle and perturbation theory.

To explore the application of quantum mechanics across a range of physical systems.

To present simple approaches to treat systems with more than one particle in quantum mechanics.

Outline Of Syllabus

Formal structure of quantum mechanics: quantum-mechanical postulates, Hermitian operators, finite- and infinite-dimensional Hilbert spaces, measurement in quantum mechanics, time evolution & Ehrenfest’s theorem

Operator algebras: harmonic oscillator; angular momentum; spin.

Many particle systems: identical particles & exchange symmetry; bosons, fermions and spin statistics theorem.

Approximation Methods: the variational principle; Rayleigh-Ritz method; time independent perturbation theory; time dependent perturbation theory.

Intended Knowledge Outcomes

To understand and be able to express the operator postulates and the formal structure of quantum mechanics.

To know the key approximation methods in quantum mechanics.

To understand simple approaches to the quantum treatment of systems with more than one particle.

Intended Skill Outcomes

To be able to state, explain the physical basis of, and apply operators and the formal structure of quantum mechanics at a mathematical level.

To be able to apply the mathematical framework of quantum mechanics to physics problems.

To be able to apply and critically evaluate approximation methods in quantum mechanics.

To be able to use and interrogate simple many-particle approaches.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples of problem solving, 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 problem solving aspects of the assessment enable students to demonstrate that they are able to apply this understanding and their analysis and synthesis skills to novel situations. Problems are set and assessed during the module to enhance the understanding of the material and nurture the progressive acquisition of skills in solving illustrative problems.

General Notes

N/A