Constructing Wave Functions Using Mathematical Reasoning

Abstract

Transfer of structural math knowledge to physics is difficult for students. While research suggests various improvement techniques, enhancing parallelism of algebraic structures used in physics to those studied in mathematics courses seems underrepresented. This paper proposes an alternative way of introducing wave functions as a set of parametric equations. Research shows that the mathematical underpinnings of the mechanical wave function are problematic for students. As seen from the math perspective, there can be several drawbacks that likely impede scientific analysis and interpretation of the wave function: y(x,t)=A cos(2πλx−2πTt).