Since its birth in the 1920s, quantum mechanics has motivated and advanced the analysis of linear operators. In this effort, it significantly contributed to the development of sophisticated mathematical tools in spectral theory. Many of these tools have also found their way into classical fluid mechanics and enabled elegant and effective solution strategies as well as physical insights into complex fluid behaviors. This review provides supportive evidence for synergistically adopting mathematical techniques beyond the classical repertoire, both for fluid research and for the training of future fluid dynamicists. Deeper understanding, compelling solution methods, and alternative interpretations of practical problems can be gained by an awareness of mathematical techniques and approaches from quantum mechanics. Techniques such as spectral analysis, series expansions, considerations on symmetries, and integral transforms are discussed, and applications from acoustics and incompressible flows are presented with a quantum mechanical perspective.

中文翻译：

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受量子力学数学方法启发的线性流分析

自 20 年代诞生以来，量子力学推动并推进了线性算子的分析。在这一努力中，它为谱理论中复杂数学工具的发展做出了重大贡献。其中许多工具还融入了经典流体力学，并实现了优雅而有效的解决策略以及对复杂流体行为的物理洞察。这篇综述为协同采用经典技能之外的数学技术提供了支持证据，无论是用于流体研究还是未来流体动力学家的培训。通过了解量子力学的数学技术和方法，可以获得更深入的理解、令人信服的解决方法以及对实际问题的替代解释。讨论了谱分析、级数展开、对称性考虑和积分变换等技术，并从量子力学的角度介绍了声学和不可压缩流的应用。