Proposing the 'IN Sign' for Enhanced Schrodinger's Equation in Quantum Mechanics

This study proposes an addition to Schrodinger'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 Schr?dinger'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.