Quantum Mechanics II - MAT00025H

«Back to module search

Related modules

Additional information

Pre-requisite modules for Natural Sciences students:

• MAT00026I Linear Algebra
• MAT00034I Applied Mathematics

OR

• MAT00036I Applied Mathematics Option 1

 

Module will run

Occurrence	Teaching period
A	Spring Term 2022-23

Module aims

This module aims to expand students’ knowledge in quantum mechanics and enable them to apply the theory of quantum mechanics more widely through approximation methods. It also aims to enable them to appreciate the deeper mathematical structure of quantum mechanics and to provide the foundation for Quantum Field Theory in stage 4.

Module learning outcomes

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

• Understand the mathematical structure of quantum mechanics.

• Understand the role of symmetries played in quantum mechanical systems.

• Be able to identify and use suitable approximation methods for energy eigenvalue problems in quantum mechanics that cannot be solved exactly.

• Be able to calculate transition probabilities in simple time-dependent quantum systems.

Module content

Syllabus

• The space of states in quantum mechanics; Hermitian and unitary operators; projection operators; observables; measurement postulates; compatible and incompatible observables.

• The representations of the angular-momentum algebra ; spherical harmonics; the spin angular momentum; the relationship between SU(2) and SO(3).

• Symmetries in quantum mechanics: Stone’s theorem (without proof); the momentum and angular-momentum operators as generators of symmetries; discrete symmetries.

• The time-evolution operator: the Schrödinger and Heisenberg pictures.

• Systems of identical particles: bosons and fermions.

• Approximation methods for the time-independent Schrödinger equation: time-independent perturbation theory (first order); the variational method..

• Dirac’s delta function; momentum eigenstates in three dimensions.

• Time-dependent perturbation theory; transition probability to first order.

Academic and graduate skills

• Academic skills: students will develop their calculus and algebra skills further in the context of a theory essential in describing the physical world at the microscopic level.

• Graduate skills: through lectures, problems classes and seminars, students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They develop problem-solving skills and learn how to apply techniques to unseen problems.

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

R Shankar, Principles of Quantum Mechanics, Springer (U 0.123 SHA)

S Gasiorowicz, Quantum Physics (2nd edition), J. Wiley.

L I Schiff, Quantum Mechanics, McGraw-Hill (U 0.123 SCH)