Probability-Preserving Transformer for the Time-Dependent Schrodinger Equation

arXiv:2608.15112v1 Announce Type: new Abstract: Solving the time-dependent Schrodinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods.

Source: arXiv cs.LG | 2026-08-18