Quantum-Frequency Fast Charging of Lithium-ion Batteries: A Theoretical Framework Based on the Schrödinger Momentum Equation

We establish a quantum-mechanical theory for describing the microscopic dynamics of individual lithium ions during the charging of lithium-ion batteries. By combining the Schrödinger Momentum Equation derived from New Quantum Mechanics with the Stefan-Maxwell formulation of concentrated-solution electrochemistry, we formulate a microscopic–macroscopic dynamical equation that couples the motion of individual lithium ions in the electrolyte to the externally imposed electric-potential gradient during battery charging. The resulting theoretical framework provides a quantitative basis for understanding how the temporal characteristics of a macroscopic charging field influence microscopic lithium-ion transport and, consequently, the overall charging dynamics. On the basis of this theory, we identify the physical mechanism underlying conventional direct-current (DC) charging and show why a constant charging potential fundamentally limits the efficiency of sustained high-rate lithium-ion transport. To overcome this limitation, we propose a quantum-frequency charging (QFC) method, in which the charging potential is modulated according to the quantum characteristic of lithium-ion motion. Theoretical analysis indicates that, compared with conventional DC charging, QFC can greatly increase the effective charging duration, maintain more continuous energy transfer, and suppress heat generation during the charging process. These results provide a theoretical foundation for a new electrochemical potential gradient paradigm based on the dynamic matching between the externally applied electric field and the intrinsic microscopic dynamics of lithium-ion transport, offering a potential route toward substantially faster and more thermally efficient lithium-ion battery fast charging.