Semiclassical Wave Packets on Riemannian Manifolds

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URI: http://hdl.handle.net/10900/83880
http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-838804
http://dx.doi.org/10.15496/publikation-25270
Dokumentart: PhDThesis
Date: 2018-08-29
Language: English
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Mathematik
Advisor: Teufel, Stefan (Prof. Dr.)
Day of Oral Examination: 2016-11-18
DDC Classifikation: 500 - Natural sciences and mathematics
510 - Mathematics
530 - Physics
Keywords: Mathematik , Mathematische Physik , Zeitabhängige Schrödinger-Gleichung , Riemannscher Raum , Approximation , Wellenpaket
Other Keywords:
Time-dependent Schrödinger equation
Approximation
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Abstract:

In this work semiclassical Gaussian wave packets are introduced and it is shown that they are approximate solutions to the Schrödinger equation in semi-classical scaling on Riemannian manifolds of bounded geometry. Furthermore it is proved that they are an approximation to the full solution and first error bounds are given.

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