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

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.