Operating mode of Fourier series and transforms in molecular dynamics

Summary: This article explores the use of Fourier series and transforms in the context of molecular dynamics. The Fourier transform is a powerful tool for analyzing random phenomena such as molecular motions and incoherent radiation. Starting from Schrödinger's formulation and concepts from quantum mechanics, the article highlights how Fourier series allow molecular motions to be decomposed into oscillations of different frequencies. Experimental results, often obtained from macroscopic samples, are compared with theoretical predictions, illustrating the challenges inherent in the study of dynamical systems. Practical applications, such as vibration analysis, X-ray diffraction, and second harmonic generation, are also discussed, highlighting the importance of these analytical methods. Finally, the article suggests perspectives for future research, particularly on the impact of molecular characteristics on random phenomena, thus strengthening the link between theory and experiment in chemistry and physics.