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arXiv · 2602.12626

Quantum Hermite functions and Fourier Transform of operators

Rahul Garg·Sundaram Thangavelu
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Abstract

We construct operator analogues of Hermite functions which form an orthonormal basis for the Hilbert space $ \mathcal{S}_2$ of Hilbert-Schmidt operators on $ L^2(\R^n).$ We use this orthonormal basis to define Fourier transform on $ \mathcal{S}_2 $ and study some of its basic properties.

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Rahul Garg, Sundaram Thangavelu. 2026-02-13. Quantum Hermite functions and Fourier Transform of operators. https://arxiv.org/abs/2602.12626

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