An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿

aygun, murat; Köksal, Koray

An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿

Murat AYGÜN, (Bitlis Eren Üniversitesi, Fizik Bölümü, Bitlis, Türkiye)

Koray KÖKSAL (Bitlis Eren Üniversitesi, Fizik Bölümü, Bitlis, Türkiye)

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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Yıl: 2020 Cilt: 9 Sayı: 2 Sayfa Aralığı: 584 - 591 Metin Dili: İngilizce İndeks Tarihi: 18-11-2020

An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿

Öz:

In the current study, we introduce an analytical form of the solution for the potential family 𝑽(𝒓) =𝑨𝒓𝟐 −𝑩𝒓+ 𝑪𝒓𝜿.The method which combines the perturbation theory (PT) and supersymmetric (SUSY) quantum theory results inan abstract equation of the energy eigenvalues (which can be named as closed analytical form method (CAFM)).The results of the asymptotic iteration method (AIM) and CAFM will be compared with the numerical method(NM) to test the validity of our approximation at the end of the work.

Anahtar Kelime:

𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿 Potansiyel Ailesinin Özdeğerlerini Veren Analitik İfade

Öz:

Bu çalışmada, 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿 potansiyel ailesine ait çözümleri veren analitik bir ifade önerdik. Süpresimetrik kuantum teorisi ile pertürbasyon teorisini birleştiren bu metod enerji özdeğerlerini içeren bir denklem sağlamaktadır (metod kapalı analitik form olarak adlandırılabilir). Çalışmanın sonunda yaklaşımımızın geçerliliğini tespit etmek için, asimptotik iterasyon metodu ve kapalı analitik form metoduna ait sonuçlar nümerik metodla karşılaştırılacaktır.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	aygun m, Köksal K (2020). An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. , 584 - 591.
Chicago	aygun murat,Köksal Koray An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. (2020): 584 - 591.
MLA	aygun murat,Köksal Koray An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. , 2020, ss.584 - 591.
AMA	aygun m,Köksal K An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. . 2020; 584 - 591.
Vancouver	aygun m,Köksal K An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. . 2020; 584 - 591.
IEEE	aygun m,Köksal K "An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿." , ss.584 - 591, 2020.
ISNAD	aygun, murat - Köksal, Koray. "An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿". (2020), 584-591.

APA	aygun m, Köksal K (2020). An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 9(2), 584 - 591.
Chicago	aygun murat,Köksal Koray An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 9, no.2 (2020): 584 - 591.
MLA	aygun murat,Köksal Koray An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol.9, no.2, 2020, ss.584 - 591.
AMA	aygun m,Köksal K An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2020; 9(2): 584 - 591.
Vancouver	aygun m,Köksal K An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2020; 9(2): 584 - 591.
IEEE	aygun m,Köksal K "An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿." Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 9, ss.584 - 591, 2020.
ISNAD	aygun, murat - Köksal, Koray. "An Analytical Expression for The Eigenvalues of The Potential Family 𝑽(𝒓) = 𝑨 𝒓 𝟐 − 𝑩 𝒓 + 𝑪𝒓 𝜿". Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 9/2 (2020), 584-591.