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arXiv · 2506.15992

Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case

Weiwei Wang·Xianchao Wu
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Abstract

This paper investigates the upper bound of the integral of $L^2$-normalized joint eigenfunctions over geodesics in a two-dimensional quantum completely integrable system. For admissible geodesics, we rigorously establish an asymptotic decay rate of $O(h^{1/2})$. This represents a polynomial improvement over the previously well known $O(1)$ bound.

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Weiwei Wang, Xianchao Wu. 2025-06-19. Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case. https://arxiv.org/abs/2506.15992

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