Modulation-Based Field Theory: A Unified Approach to Quantum Mechanics

This paper introduces an auxiliary modulation coordinate framework for understanding quantum mechanics, demonstrating that quantum evolution can be viewed as a structured energy flow rather than solely a probabilistic process. By deriving Schrödinger's equation from the fundamental energy propagation equation of the auxiliary modulation coordinate, we show that quantum mechanics can be understood as an emergent boundary effect of structured energy interactions. The presence of force modulation, potential structuring, and deterministic oscillations within this framework confirms that quantum interactions adhere to predefined energy constraints. Additionally, the application of entropy-resolved resonance profiles eliminates the necessity for iterative wave collapse, reinforcing that quantum resolution is inherently structured. This work formally redefines quantum mechanics as the study of structured energy flow at observable scales, providing an alternative perspective to the traditional probabilistic interpretation. For those interested in applying or exploring the theory further, readers are welcome to reach out with specific questions.