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Session S30 - Mathematical Methods in Quantum Mechanics

Monday, July 19, 20:00 ~ 20:40 UTC-3

Direct and inverse Sturm-Liouville problems: A method of solution

Vladislav Kravchenko

Cinvestav, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will present some recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals which result in a new approach for solving direct and inverse spectral and scattering problems [1]. The approach is based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. [1] V. V. Kravchenko Direct and inverse Sturm-Liouville problems: A method of solution. Birkhäuser, Series: Frontiers in Mathematics, 2020.

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