The University of Southampton
Courses

## Module Overview

This course will cover advanced topics of quantum mechanics including postulates of quantum mechanics, tools of quantum mechanics, Dirac notation, Simple Harmonic oscillator (studied using raising and lowering operators), orbital and spin angular momentum (studied using raising and lowering operators), Density matrix and Schroedinger's cat, Non-locality and the Bell inequalities, Quantum cryptography (distributing secure keys), basic ideas of Quantum computing (qubits, quantum teleportation). (Last 4 topics non examinable in final assessment, only in problemsheets).

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Be able to work with operators and states using Dirac's bra and ket notation
• Study the simple harmonic oscillator using raising and lowering operators
• Understand quantum angular momentum, including spin, and analyse it using raising and lowering operators
• Understand non-locality and the Bell inequalities, and apply the concepts to cryptographic key exchange
• Understand qubits and some basic ideas in quantum computation

### Syllabus

- Postulates of quantum mechanics - Tools of quantum mechanics (vector spaces, operators and states) - Dirac notation - Simple Harmonic oscillator (studied using raising and lowering operators) - Orbital and spin angular momentum (studied using raising and lowering operators) - Adding angular momenta - Density matrix and Schoedinger's cat - Non-locality and the Bell inequalities - Quantum cryptography (distributing secure keys) - Basic ideas of Quantum computing (qubits, quantum teleportation)

### Learning and Teaching

TypeHours
Preparation for scheduled sessions18
Revision10
Lecture36
Follow-up work18
Total study time150

JJ Sakurai (1994). Modern Quantum Mechanics.

R Shankar (1994). Principles of Quantum Mechanics.

S Gasiorowicz (1996). Quantum Physics.

RP Feynman et al (1970). Feynman Lectures on Physics.

### Assessment

#### Assessment Strategy

Weekly problem sheets will be set, with the worst two waived. In an instance where a student may miss submitting one or two problem sheets, those sheets will not be counted. Students are required to submit Self Certification forms on time for all excused absences, as you may ultimately end up missing 3+ problem sheets through due for example to illness. The submitted Self Certification forms may be considered as evidence for potential Special Considerations requests to get waived more than standard two problemsheets. Please note that documentary evidence will normally be required before these can be considered. Last four topics in the syllabus will not be examinable in final assessment, only in problem sheets.

#### Summative

MethodPercentage contribution
Continuous Assessment 10%
Final Assessment  90%

#### Repeat

MethodPercentage contribution

#### Referral

MethodPercentage contribution