Quantum Wave Resistance of Schrodinger functions

TL;DR

This paper introduces the concept of quantum wave-impedance (QWI) for Schrödinger functions, revealing its properties, relation to fundamental constants, and potential significance in future quantum technologies.

Contribution

It defines quantum wave-impedance as an analogue to electromagnetic impedance, linking it to quantum numbers and fundamental constants, and explores its implications for quantum transport and technology.

Findings

Quantum impedance is generally non-zero and resistive for free particles.

Z relates to fundamental constants like the fine structure constant.

Z exhibits peaks, valleys, and plateaus as functions of quantum numbers.

Abstract

The new concept of quantum wave-impedance (QWI), Z is introduced to answer the question whether there is impedance to a Schrodinger wave. Z will be an analogue of Maxwell's free space impedance (376.7 ohm) for electromagnetic waves. We show, for free particle wave function, the value of Z is in general not zero and purely real (resistive). As in quantum hall (QHE), Z can be expressed in terms of the fine structure constant, the electromagnetic permittivity and permeability of free space. Z is a determinant of the partitioning and flow of charge and energy transported by the quantum system. The scale factor of Z is about 12.9 kilo-ohms (per spin), so the corresponding wave conductance G is (77.5 micro-mho, per spin) double the unit of Landaur conductance. As functions of the quantum numbers (l,m,n) Z shows, peaks, valleys and plateaus; also as in QHE, both integer and fractional steps may be obtained. In microwave and optical technology, conventional impedance is an essential parameter. The quantum impedance defined here will be no exception in future technology.