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MATH 429 Functional Analysis and Quantum Mechanics Units: 3.00
A generalization of linear algebra and calculus to infinite dimensional spaces. Now questions about continuity and completeness become crucial, and algebraic, topological, and analytical arguments need to be combined. We focus mainly on Hilbert spaces and the need for Functional Analysis will be motivated by its application to Quantum Mechanics.
Learning Hours: 132 (36 Lecture, 12 Group Learning, 84 Private Study)
Requirements: Prerequisite ([MATH 110/6.0 or MATH 111/6.0* or MATH 112/3.0] and MATH 281/3.0) or permission of the Department.
Offering Faculty: Faculty of Arts and Science
Course Learning Outcomes:
- Have experience with extensions to the mathematics of Quantum Mechanics, the Schrödinger equations, and the harmonic oscillator.
- Have foundational experience with metric spaces, Banach spaces, inner product spaces, Hilbert spaces, operators and their spectrum.
- Work with extending the concepts of Linear Algebra and Calculus to the infinite dimensional setting.
- Work with problems from Mathematical Physics and in particular with the mathematical foundations of Quantum Mechanics.