●本授業の目的およびねらい
Functional analysis is a useful tool for many physical theories, and has been partially developed concomitantly with quantum mechanics. The aim of this course is to provide the necessary background for a good understanding of the mathematics behind any course of quantum mechanics. During this one semester course, the notions of distributions, of Lebesgue integral, and the foundation of spectral theory will be introduced. Depending on the interest of the audience, different tools of spectral theory will be further developed.
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●履修条件あるいは関連する科目等
Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II.
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●授業内容
Distribution theory
Lebesgue integrals
Hilbert spaces and bounded operators
Unbounded operators
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●成績評価の方法
The final grade will be based on the active participation during the lectures and on some written reports.
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●教科書
Material will be provided during the lectures.
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●参考書
Reference books will be provided during the lectures.
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●注意事項
This course in an optional subject which does not count towards the number of credits required for graduation in any program at Nagoya University.
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●本授業に関する参照Webページ
http://www.math.nagoya-u.ac.jp/~richard/SMLfall2019.html
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●担当者からの言葉(Webページのみ表示)
Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.
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