Quantum Tunneling Through a Mode-Quantized Barrier: A Dynamical Second-Quantization Framework

Quantum tunneling is conventionally described by the Schrödinger wave equation with a prescribed static potential barrier, providing accurate transmission probabilities but offering limited insight into the microscopic dynamics of particle–barrier interactions. In this work, we develop a dynamical second-quantization framework in which the barrier is modeled as an ensemble of quantized internal modes rather than as an externally imposed classical potential. The tunneling particle interacts directly with these microscopic barrier excitations through a coupled particle–barrier Hamiltonian, from which the Heisenberg equations of motion are derived. Collective coherent excitations of the barrier modes give rise to an emergent effective barrier that naturally recovers the conventional rectangular barrier and the WKB transmission limit under appropriate conditions. Unlike standard treatments, the present formulation explicitly incorporates microscopic barrier dynamics and provides a unified description of particle–barrier coupling within a second-quantized formalism. The framework further suggests that repeated tunneling events may experience different microscopic interaction histories, motivating a statistical interpretation of tunneling times. Because both the particle and barrier are treated within the same operator formalism, the theory provides a natural foundation for extension to relativistic quantum transport, photonic barriers, cavity quantum electrodynamics, and other structured quantum media.