Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Access type: Open accessPublisher: search.filters.publisher.Frontiers Media S.A.

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  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    A Perturbative Approach To the Tunneling Phenomena
    (Frontiers Media S.A., 2019) Erman, Fatih; Turgut, Osman Teoman
    The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely path-integral, WKB, and instanton calculations. All these methods are non-perturbative and there is a common belief that it is dif fi cult to fi nd the splitting in the energy due to the barrier penetration from a perturbative analysis. However, we will illustrate by explicit examples including singular potentials (e.g., Dirac delta potentials supported by points and curves and their relativistic extensions) it is possible to fi nd the splitting in the bound state energies by developing some kind of perturbation method.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    The Propagators for Δ and Δ′ Potentials With Time-Dependent Strengths
    (Frontiers Media S.A., 2020) Erman, Fatih; Gadella, Manuel; Uncu, Haydar
    We study the time-dependent Schrodinger equation with finite number of Dirac delta and delta ' potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrodinger equation for delta ' potential with particular forms of the strengths.