Complete-Current Estimates for Coherent Quantum Sources and Continua

How can an approximation to a quantum wave be converted into a reliable estimate of physical transport when coherent sources, singular interactions, and continuous spectra remain part of the dynamics? This paper develops quantitative response and probability-current estimates that retain the complete quantum source, interference terms, and reciprocal feedback. The results connect temporally regular forcing to response bounds that control the derivatives needed for physical currents. They include finite spectral-window estimates for varying coherent inputs, ordered resolvent identities for noncommuting energy weights, and complementary spatial-force and temporal-regularity methods. Bound-state poles and continuum contributions are retained explicitly, together with endpoint, localization, and source-regularity costs. A worked application treats a Coulomb electron coupled to a dynamical quantum oscillator through a smooth compact interaction profile. It derives the complete Coulomb forcing measure and establishes quantitative spectral and finite-time estimates for the coupled model. The analysis controls both electron and source currents without replacing the source by a classical expectation or discarding its feedback. Appendices develop forcing compression with all sources retained and demonstrate why a small omitted source contribution need not imply negligible causal feedback. These results supply explicit analytic inputs for quantum transport and measurement-record analysis. The current bounds are not themselves event probabilities. Such probabilities, and a physically realized measurement apparatus, require additional flow, preparation, and decoder assumptions.