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The Discrete Schrödinger Equation with Quasi Periodic Potential
KTH, School of Engineering Sciences (SCI).
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Den Diskreta Schrödingerekvationen med Kvasiperiodisk Potential (Swedish)
Abstract [en]

In this paper we investigate the discrete and time independent Schrödinger equation with a quasi periodic potential.  Our purpose  is  to  investigate  the  differences  between  a Schrödinger equation  with  periodic  potential  and  Schrödinger  equation with quasi periodic potential.  We show in a specific case that if the potential function is quasi periodic then there can exist non-trivial  normalizable  solutions  to  the  discrete  Schrödinger equation  (in contrast  to  the  case  when  the  potential  is  peri- odic).  We also find a lower bound for the maximal Lyapunov exponent of  the  same  system.   Finally  we  show  that  certain Schrödinger  equations  will  always  have  a  maximal  Lyapunov exponent that is even with respect to energy.

Abstract [sv]

I den här texten så  undersöks den diskreta och tidsoberoende Schrödingerekvationen med en kvasiperiodisk po tential. Syftet med texten är att undersöka skillnaden mellan  en Schrödingerekvation  med  periodisk  potential  och  en Schrödingerekvation  med kvasiperiodisk  potential.    Vi  visar i ett specifikt fall att om potentialen är kvasiperiodisk såkan det  existera  icketriviala  och  normaliserbara  lösningar  till  den diskreta  Schrödingerekvationen  (till  skillnad  fr˚an  fallet  med periodisk potential).  Vi hittar ocksåen undre begränsning av den  maximala  Lyapunovexponenten  för  samma  system.   Till sist  så visar vi att vissa Schrödingerekvationer alltid har en maximal Lyapunovexponent som är  jämn med hänseende på energi.

Place, publisher, year, edition, pages
2018. , p. 50
Series
TRITA-SCI-GRU ; 2018-100
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-231555OAI: oai:DiVA.org:kth-231555DiVA, id: diva2:1229201
Supervisors
Examiners
Available from: 2018-06-29 Created: 2018-06-29 Last updated: 2018-06-29Bibliographically approved

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  • apa
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