Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/11990
Title: Perturbative and exact analysis of point interactions
Other Titles: Noktasal etkileşimlerin pertürbatif ve tam analizi
Authors: Erman, Fatih
Altınbaşak, Ezgi
Izmir Institute of Technology
Keywords: Point interactions
Dirac delta potentials
Perturbation theory
Issue Date: Dec-2021
Publisher: Izmir Institute of Technology
Abstract: In this thesis, a general formulation for the bound state energies of a finite number of attractive Dirac delta potentials is given in terms of a finite dimensional matrix. The stationary scattering problem is also studied using the distributional solutions of algebraic equations in momentum space. Finally, the energy gap and splitting for the bound state energies when the distance between the delta potentials is large is approximately calculated using a kind of perturbation theory.
Bu tezde, sonlu sayıda çekici Dirac delta potansiyellerinin bağlı durum enerjileri için genel bir formülasyon sonlu boyutlu bir matris cinsinden ifade edilmiştir. Ayrıca, durağan saçılma problemi momentum uzayında yazılmış cebirsel denklemlerin dağılımsal çözümleri kullanılarak çalışılmıştır. Son olarak delta potansiyelleri arasındaki mesafe büyük olduğunda bağlı durum enerjilerindeki değişim ve ayrışma, bir çeşit pertürbasyon teorisi kullanılarak yaklaşıkça hesaplanmıştır.
Description: Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2021
Includes bibliographical references (leaves. 66-71)
Text in English; Abstract: Turkish and English
URI: https://hdl.handle.net/11147/11990
Appears in Collections:Master Degree / Yüksek Lisans Tezleri

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