The infinite square well in a reformulation of Quantum mechanics without potential function

TL;DR

This paper demonstrates how to analytically derive the energy spectrum and wave functions of an infinite square well using a reformulated quantum mechanics approach that does not require a potential function, establishing correspondence with standard methods.

Contribution

It introduces a potential-free reformulation of quantum mechanics applied to the infinite square well, providing an analytical solution and linking it to traditional formulations.

Findings

Analytical energy spectrum obtained without potential function

Wave functions derived in the reformulated approach

Established correspondence with standard quantum mechanics

Abstract

Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work constitutes an example of how to establish the correspondence between this approach and the standard formulation of quantum mechanics.