Circuit Theory Based on New Concepts and Its Application to Quantum Theory 34. Algebraic Invariants Expression of One-Dimensional Wave Functions Is J-Unitary Matrix Showing Losslessness
Year: 2024
Type: article
Abstract: Heaviside proposed the telegrapher's equations as an alternative to Maxwell equations and obtained the solution of the telegrapher's equations by the operator method. Indeed, the solution was a one-dimensional wave function. One-dimensional wave equations are partial differential equations and are conventionally solved as initialvalue and boundary-value problems in mathematics. Heaviside's solution was found to be related to the algebraic invariants studied in mathematics in the 19th century. From algebraic invariants, lossless circuits were obtained as Junitary matrix. These research findings are still under study. To utilize the research achievements effectively, the application of lossless circuits obtained from algebraic invariants to quantum physics is one of the issues to be studied in the future.
Source: Journal of Signal Processing
DOI: 10.2299/jsp.29.19
Authors: Nobuo Nagai, Hirofumi Sanada, Takashi Yahagi
Institutions: Hokkaido University, Hokkaido University of Science
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Hokkaido University
OpenAlex ID: W4405929901