Direct Quantum Inversion: Reconstructing Underlying Dynamics from Kinematical Ensemble Measurements
Abstract
This work demonstrates that quantum kinematics—characterized by a system's probability density or wavefunction—inherently encodes the underlying dynamics governing its temporal evolution. We show that these quantum dynamical underpinnings can be systematically uncovered through the direct quantum inversion of probability densities measured across a well-prepared, pure, ground-state ensemble. If multiple density and potential functions fit the data and survive the framework’s statistical screening, spectroscopic studies of excited states resolve the deadlock unambiguously. This study highlights the prospect of discovering and formulating physical laws directly within the quantum framework, bypassing the historical reliance on classical physics to supply potential energy functions. Furthermore, this direct inversion approach is uniquely suited for modeling purely quantum systems that lack macroscopic classical counterparts. Finally, we validate the practical application, viability, and physical implications of this framework using several synthetic and analytical examples.
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