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# Quantum Mechanics II - MAT00025H

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• Department: Mathematics
• Module co-ordinator: Prof. Atsushi Higuchi
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2020-21

## Related modules

• None

### Prohibited combinations

• None

Pre-requisite modules for Natural Sciences students:

• MAT00026I Linear Algebra
• MAT00034I Applied Mathematics

OR

• MAT00036I Applied Mathematics Option 1

## Module will run

Occurrence Teaching cycle
A Spring Term 2020-21

## 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 (reminder); 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; the variational method; the WKB approximation.

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

• 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.

## Assessment

Task Length % of module mark
University - closed examination
Quantum Mechanics II
2 hours 100

None

### Reassessment

Task Length % of module mark
University - closed examination
Quantum Mechanics II
2 hours 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.