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arXiv · 2608.15112

Probability-Preserving Transformer for the Time-Dependent Schr\"odinger Equation

Mushtaq Ali·Muzamil Tariq·Niaz Ali Khan
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Abstract

Solving the time-dependent Schr\"odinger 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.

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Mushtaq Ali, Muzamil Tariq, Niaz Ali Khan. 2026-08-15. Probability-Preserving Transformer for the Time-Dependent Schr\"odinger Equation. https://arxiv.org/abs/2608.15112

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