Quantum Dynamics via Score Matching on Bohmian Trajectories
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 Schrödi...
| Authors | Lei Wang |
|---|---|
| Primary category | quant-ph |
| Published | 28 April 2026 |
| Last updated at source | 28 April 2026 |
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