Manuel Cañizaresek bere tesia defendatuko du urriaren 16an

• Defentsa Leioako Campuseko Zientzia eta Teknologia Fakultateko Gradu Aretoan egingo da

Manuel Cañizaresek Fisika eta Matematika ikasi zituen Sevillako Unibertsitatean, eta gero Fisika Matematikoko master bat Granadako Unibertsitatean. Haien interesak fenomeno fisikoak zorroztasun matematikoz ulertzera bideratuta egon dira beti. Cañizaresek doktoregoko ikasle gisa lan egiten du Basque Center for Applied Mathematics-en (BCAM), Analisi Harmonikoa eta alderantzizko arazoak (HA) ikerketa taldean.

Bere tesia, Hamiltoniar kuantikoen identifikazioa interakzio elektrikoen aurrean. Ikuspegi analitikoa Pedro Caroren (BCAM eta Ikerbasque) ikuskaritzapean dago.

Defentsa urriaren 16rako (asteazkena) programatuta dago, Leioako Campuseko Zientzia eta Teknologia Fakultateko Gradu Aretoan, 15: 00etan.

BCAMeko kide guztien izenean, Manueli zorterik onena opa nahi diogu bere tesiaren defentsan.

Abstract

In this thesis, we consider two inverse problems motivated by physical models related to quantum mechanics, particularly with the Schrödinger equation. These are the scattering problem with local near-field data and the problem of initial-to-final data in quantum mechanics. In both cases, we obtain an analytical uniqueness result related to the possibility of identifying time-independent electric potentials.

In the first problem, we demonstrate that potentials existing in functional spaces of low regularity can be identified by placing point sources and measuring the scattered wave at constant energy on small pieces of hypersurfaces near the support of the potential, in dimensions n≥3n \geq 3. To achieve this, we use harmonic analysis methods, domain perturbation techniques, and we prove a Runge approximation result.

In the second problem, we obtain a uniqueness result for bounded potentials with polynomial decay in dimensions n≥2n \geq 2. However, in this case, we do this by measuring the final state of a quantum system that interacts with the potential for every possible initial state.