2023 年 27 巻 1 号 p. 29-34
Abstract Partial reflection is an electromagnetic phenomenon that occurs concurrently with refraction, but the presence of partial reflection is ignored in the variational calculus, which is frequently used to analyze electromagnetic phenomena in physics. In mathematics, Fuchs functions were derived from wave equations without considering partial reflection, and modular forms were then derived from the Fuchs functions. It is shown in this session that the cascade matrices used in circuit theory are expressed using two functions with duality, that is, voltage and current, serve as a mathematical tool expressed by a linear combination existing in an identical space, and have a modular form. In future work, it is expected that new functions and actions of the cascade matrices with a modular form and duality can be clarified through their application to electromagnetics and quantum mechanics.
