Spectral Emission and Wavefunction Dynamics from Electromagnetic Cavity Resonances Part II: The Dynamic Envelope Limit

We demonstrate that two fundamental features of quantum atomic physics---spectral emission frequencies and the Schrodinger equation---emerge naturally as the dynamic limits of classical electromagnetic field confinement. This work builds directly on the geometric boundary condition established in Part I ($r_p = 4\hbar/m_p c$), where the electron mass and Rydberg constant were derived from field tension and vacuum response \cite{collins2025}. Here, we address the dynamics of this confinement. We show that photon emission arises from the mechanical beat frequency between interfering cavity modes, and that the Schrodinger equation is the slow-envelope limit of Maxwell's equations under the non-relativistic approximation. Numerical simulations confirm that the Lyman-$\alpha$ transition frequency is reproduced to $<0.01\%$ error when the cavity is parameterized by the geometrically derived constants. Fast Fourier Transform (FFT) analysis of the time-dependent dipole moment validates the beat frequency mechanism, while finite-difference eigenvalue solving demonstrates that the envelope equation recovers the quantum harmonic oscillator spectrum exactly. This work provides a deterministic, geometric foundation for quantum dynamics, suggesting that the wavefunction describes the effective envelope of confined electromagnetic fields at timescales much longer than the Compton period.