Abstract
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.