Circuit Theory Based on New Concept and Its Application to Quantum Mechanics

Nobuo Nagai, Takashi Yahagi

Nobuo Nagai, Takashi Yahagi

The Schrödinger equation is derived from the concept that particles of matter such as electrons have a wave nature, and it is used to express phenomena specific to quantum mechanics, such as the advancing wave and the quantum tunneling effect. In this session, we apply circuit theory to the Schrödinger equation and define voltage and current using wave functions that satisfy the Schrödinger equation. By this method, we show that a lossless transmission line or circuit can be obtained. Thus, a circuit that satisfies the Schrödinger equation is lossless and is not directly related to heat, but the reactive power is related to the regulation of energy. Therefore, such a circuit can be discussed in a theoretical system that does not rely on probability theory.

Russer

Nobuo Nagai, Hirofumi Sanada, Takashi Yahagi

Circuit theory, which explains the behavior of electromagnetic waves, concerns reflection waves caused by the difference in impedance. In this session, we demonstrate that electromagnetic waves with the angular frequency of nπ or nπ + π/2 exhibit interesting behavior in circuits with a high impedance ratio and a large amount of reflection. The physical phenomenon of increasing the amount of reflection is considered to be the same as the tunneling effect in quantum mechanics. This demonstration shows that the application of the telegrapher's equations expressing the electromagnetic fields and waves of the Maxwell equations to quantum mechanics may provide a clue to seeing the light at the end of the mysterious tunnel in quantum mechanics.

Nobuo Nagai, Takashi Yahagi

In Session 8, we demonstrated that circuit theory can be applied to the Schrödinger equation, a basic equation in quantum mechanics. In this session, we attempt to apply circuit theory to the Dirac equation using the Riccati differential equation and demonstrate that physical phenomena such as spin 1/2 can be explained on the basis of circuit theory. To this end, we obtain the one-dimensional Dirac equation for the complex equivalent circuit for a physical phenomenon. We show that the Dirac equation can be regarded as a type of low-energy effective field theory in quantum theory and that circuit theory can be applied to the Dirac equation.

Paul L. Kelley, Benjamin Lax, Peter E. Tannenwald