Undergraduate Course: Quantization (MATH11139)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This is an introductory quantum theory course aimed at Mathematics students. It emphasises the mathematical structures which will be illustrated in simple physical systems, such as the harmonic oscillator and finite-dimensional spin systems. The course provides the language and tools for the study of modern topics such as quantum information and quantum computation. |
| Course description |
- Basic notions of Hilbert spaces (both finite- and infinite-dimensional)
- Axioms of quantum theory (states, operators, probabilistic interpretation, time evolution)
- Heisenberg uncertainty principle
- Simple examples of finite-dimensional quantum systems
- Canonical quantisation
- Stone-von Neumann theorem
- The quantum harmonic oscillator and the correspondence principle
- Groenewold-Van Hove theorem and deformation quantisation (examples)
- Density matrices, entanglement, von Neumann entropy
- Bell's inequalities
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
- Explain the axioms of quantum theory
- Ability to calculate quantities such as probabilities, expectation values and time-evolution of states in simple quantum systems, both in the standard operator language and using density matrices
- Ability to solve for the spectrum of the harmonic oscillator - Ability to calculate entanglement entropy in simple finite-dimensional quantum systems
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Reading List
Recommended:
Nielsen & Chuang - Quantum computation and quantum information, CUP 2000
Preskill - Lectures on Quantum Computation (available online) |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Qua |
Contacts
| Course organiser | Dr Thomas Leinster
Tel: (0131 6)50 5057
Email: Tom.Leinster@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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