Abstract:We solve the time-dependent Schrödinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under the classical potential supplemented by a quantum potential depending on the score function of the evolving density. These non-crossing Bohmian trajectories form a continuous normalizing flow governed by the score. We parametrize the score with a neural network and minimize a self-consistent Fisher divergence between the network and the score of the resulting density. We prove that the zero-loss minimizer of this self-consistent objective recovers Schrödinger dynamics for nodeless wave functions, a condition naturally met in quantum vibrations of atoms. We demonstrate the approach on wavepacket splitting in a double-well potential and anharmonic vibrations of a Morse chain. By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrödinger equation to the rapidly advancing toolkit of modern generative modeling.
| Comments: | 8 pages, 5 figues, code at this https URL |
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2604.25137 [quant-ph] |
| (or arXiv:2604.25137v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2604.25137 arXiv-issued DOI via DataCite (pending registration) |
From: Lei Wang [view email]
[v1]
Tue, 28 Apr 2026 02:25:48 UTC (1,604 KB)
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