Proposing the 'IN Sign' for Enhanced Interpretations of Schrödinger's Equation in Quantum Mechanics

Abstract

This study proposes an addition to Schrödinger's equation by introducing the 'IN sign,' enabling the energy operator and wave function to interact dynamically and swap roles. This modification allows the energy operator to act within a field of waves and incorporates additional quantum states. The 'IN sign' is a step toward understanding wave function evolution across multiple variables, offering potential applications in quantum mechanics and topological studies. Purpose: This research aims to enhance Schrödinger's equation by integrating the 'IN sign,' allowing dynamic interaction between the energy operator and the wave function while extending its application to complex potentials and topological frameworks. Significance: The proposed modification has profound implications in quantum mechanics, enabling more comprehensive modeling of wave functions and their interactions across multidimensional systems.