Introducing Viewpoints of Mechanics into Basic Growth Analysis : (X) Wave Functions in Comparison and Relationship with Growth Functions

Abstract

This study was conducted to investigate wave functions derived from introducing growth jerk into basic growth mechanics by paying attention to the comparison and relationship with growth functions. Positive and negative signs, which appeared in taking the square root when solving the differential equation, gave wave functions (Ψ=(±W0)·(±exp((±iRGR)·t))) as well as growth functions (W=(±W0)· (±exp((±RGR) ·t))). The results obtained were as follows. (1) Growth functions suggested basic phenomena of ruminant agriculture through the concept of energy conservation and an open system adopted by living things that showed degradation and synthesis of body components. (2) Wave functions gave anticlockwise and clock- wise rotations. Three-dimensional coordinates suggested from wave functions gave right-handed spirals, and left-handed spirals were derived when some wave functions were given another way of description. (3) Wave functions were related with growth functions through hypothetic operations bridging the weight gap between 0 ± iW0 and ±W0. It was suggested that introducing growth jerk into basic growth mechanics gave some pieces of information about properties of wave functions in the comparison and relationship with growth functions.