Elektrik ve manyetik alanlar altında sonlu silindirik ve parabolik kuantum telinde polarizasyon
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Dosyalar
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezde, sonlu silindirik ve parabolik kuantum telinde elektrik ve manyetik alanlar altında taban durum enerjileri ve polarizasyon hesapları çalışıldı. Efektif kütle yaklaşımı kullanılarak, manyetik alan altında elektronun taban durumu için dalga fonksiyonu ve enerjisi dördüncü derece Runge-Kutta nümerik metoduyla hesaplandı. Elektrik ve manyetik alan altında yabancı atomlu ve atomsuz elektronun enerji hesapları varyasyon metodu ile yapıldı. Sonlu silindirik ve parabolik kuantum tellerine manyetik alan etkisi farklı yabancı atomlu konumlarda tel yarıçapına bağlı olarak incelendi. Sadece manyetik alanın silindirik telde parabolik tele göre daha etkili olduğu görüldü. Kuantum tellerine elektrik alanın uygulandığında taban durum enerjilerini azalttığı, yabancı atomlu ve bağlanma enerjilerinde ise yabancı atomun konumuna bağlı olarak dramatik değişimler yaptığı görüldü. Kuantum tellerinde elektrik ve manyetik alanın birlikte etkisinde enerjiler üzerinde yabancı atomun konumunun etkili olduğu görüldü. Elektrik alan değişimiyle yabancı atom yokken ve varken elektronun polarizasyonu sonlu silindirik kuantum tellerinde hızla artıp sabit değere giderken, sonlu parabolik kuantum tellerinde lineer artışlar gösterdi. Dalga fonksiyonlarına bakıldığında silindirik telde elektrik alanın daha etkili olduğu görüldü. Elektrik ve manyetik alanlar birlikte uygulandığında polarizasyonda tel yarıçapının ve yabancı atomun konumunun önemli olduğu görüldü.
abstract
In this thesis, the calculations of ground state energies and polarization were studied in finite cylindrical and parabolic quantum wires under electric and magnetic fields. By using effective mass approximation, the energy and wave function under magnetic fields were calculated for ground state of electron by fourth degree Runge- Kutta numerical method. Energy calculations of electron with and without impurity under electric and magnetic fields were done by variation method. The effect of magnetic field on finite cylindrical and parabolic quantum wires were investigated at different impurity positions depending on the wire radius. The magnetic field was only observed to be more effective in cylindrical quantum wire rather than that in parabolic quantum wire. When the electric field was applied to the quantum wires, it was observed that the ground state energies were decreased and the binding energy had dramatic changes depending on impurity position. In synergical effect of electric and magnetic fields on quantum wires, the position of impurity was observed to be effective on energies. With the electric field changing, when there was with and without impurity, the polarization of the electron in finite cylindrical quantum wire increased fast and reached fixed value, however, it showed linear increase in finite parabolic quantum wire. When the wave functions were evaluated, the electric field was observed to be more effective in cylindrical wire. The wire radius and the position of impurity were determined to be important for polarization when electric and magnetic fields were performed together.
abstract
In this thesis, the calculations of ground state energies and polarization were studied in finite cylindrical and parabolic quantum wires under electric and magnetic fields. By using effective mass approximation, the energy and wave function under magnetic fields were calculated for ground state of electron by fourth degree Runge- Kutta numerical method. Energy calculations of electron with and without impurity under electric and magnetic fields were done by variation method. The effect of magnetic field on finite cylindrical and parabolic quantum wires were investigated at different impurity positions depending on the wire radius. The magnetic field was only observed to be more effective in cylindrical quantum wire rather than that in parabolic quantum wire. When the electric field was applied to the quantum wires, it was observed that the ground state energies were decreased and the binding energy had dramatic changes depending on impurity position. In synergical effect of electric and magnetic fields on quantum wires, the position of impurity was observed to be effective on energies. With the electric field changing, when there was with and without impurity, the polarization of the electron in finite cylindrical quantum wire increased fast and reached fixed value, however, it showed linear increase in finite parabolic quantum wire. When the wave functions were evaluated, the electric field was observed to be more effective in cylindrical wire. The wire radius and the position of impurity were determined to be important for polarization when electric and magnetic fields were performed together.
Açıklama
Yüksek Lisans Tezi
Anahtar Kelimeler
The Binding Energy, The Magnetic Field, The Parabolic Wire, The Cylindrical Wire, The Polarization, The Electric Field, Bağlanma Enerjisi, Manyetik Alan, Silindirik Tel, Parabolik Tel, Polarizasyon, Elektrik Alan
