Abstract Eigenspaces of the quantum isotropic Harmonic Oscillator on have extremally high multiplicites and the eigenspace projections have special asymptotic properties. This article gives a detailed study of their Wigner distributions Heuristically, if is the “quantization” of the energy surface ΣE, and should be like the delta-function on ΣE; rigorously, tends in a weak* sense to But its pointwise asymptotics and scaling asymptotics have more structure. The main results give Bessel asymptotics of in the interior of ΣE; interface Airy scaling asymptotics in tubes of radius around ΣE, with either in the interior or exterior of the energy ball; and exponential decay rates in the exterior of the energy surface.

中文翻译：

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谐振子的本征空间 Wigner 分布的界面渐近性

摘要 量子各向同性谐波振荡器的本征空间具有极高的乘数，本征空间投影具有特殊的渐近性质。本文详细研究了他们的Wigner分布，如果是能量面ΣE的“量子化”，应该是ΣE上的delta函数；严格来说，在弱*意义上趋向于 但它的逐点渐近和标度渐近有更多的结构。主要结果给出了 ΣE 内部的 Bessel 渐近性；在 ΣE 周围半径管中的界面 Airy 标度渐近，与能量球的​​内部或外部；和能量表面外部的指数衰减率。