Aharonov-Bohm Olayı ve Monopol

Abstract

David Bohm ve doktora öğrencisi Yakir Aharonov 1959 yılında Aharonov-Bohm (AB) olayını keşfettiler. Daha sonra AB olayı 1986 yılında A. Tonomura ve arkadaşları tarafından deneysel olarak doğrulanarak daha çekici bir hale gelmiştir (Tonomura ve ark., 1982, 1986). AB olayının anlaşılması ile kuramsal fiziğin temelleri ve AB olayı ile ilgili başka fiziksel olay ve kavramlar daha iyi anlaşılmaktadır. Bu çalışmada, Aharonov-Bohm olayı incelenip tartışılmaktadır (Aharonov ve Bohm, 1959). AB olayının sonucunda, kuantum mekaniğinde elektromagnetik (EM) potansiyellerin ilginç özellikleri ortaya çıkmakta ve ayrı bir önem kazanmaktadır. Klasik mekaniğe göre, alanlar yüklü parçacıkların kendisi ile direk etkileşmektedir fakat Aharonov-Bohm olayına göre etkiyen hiçbir alan olmasa bile yüklü parçacıkların elektromagnetik potansiyellerle etkileştiği anlaşılmaktadır. Ayar dönüşümleri altında Schrödinger dalga denkleminin değişmez (invaryant) kalması, dalga fonksiyonun dönüşmesini gerektirir. Dönüşen dalga fonksiyonu bir faz çarpanı içerir ve bu faz, elektromagnetik potansiyellere bağlıdır. Önerilen Aharonov-Bohm deneyinde hiç bir alanla etkileşmeyen fakat sadece elektromagnetik potansiyeller ile etkileşen elektronlar girişim deseninde kaymaya neden olur. Bunun sonucunda, faz kayması, magnetik akı, magnetik tek-kutup (monopole) kuantizasyonu gibi önemli sonuçlar elde edilir. Ayrıca, yarı-klasik yöntemle de magnetik tek-kutup ve elektromagnetik açısal momentum kuantizasyonu yapılabilmektedir (Sakurai, 1994; Jackson, 1999) . Ayar dönüşümünün fiziksel anlamı ve vektör potansiyel hesaplarından sonra bir sarmal (selenoid) ile etkileşen yüklü parçacıkların saçılma genliği ve diferansiyel tesir kesit hesapları yapılarak, sonuçları tartışılmaktadır.

 

Keywords

• Aharonov-Bohm,Ayar Dönüşümü,Dirac Kuantizasyonu,Saçılma,Tek-kutup (Monopol)

Aharonov-Bohm Effect and Monopole

Abstract

David Bohm and his Ph.D. student Yakir Aharonov discovered Aharonov-Bohm (AB) effect in 1959. Then AB effect has been confirmed by experiment which was done by A. Tonomura and his colleagues and then it became more attractive (Tonomura and et al., 1982, 1986). By understanding AB effect, fundamental of theoretical physics and other physical phenomena which is related to AB effect, are better understood. In this study, AB effect is discussed and analyzed here (Ahoronov and Bohm, 1959). As a result of AB events, an interesting properties and significance of electromagnetic potentials are appeared in quantum theory. In classical mechanics, charged particles are interacted with the electromagnetic field itself directly. But according to AB effect, even if there is no electromagnetic fields, charged particles are interacted with the electromagnetic potentials. Schrödinger equation does not change under the gauge transformation, then wave function needs to be transformed as we know that wave function can be multiplied by a phase factor. This phase factor is depends on electromagnetic potentials and it causes quantum interference patern to shift has been observed by AB experiment, then we see that charged particles are interacted with electromagnetic potentials (not fields). As a result of these kind of events leads to phase shift, magnetic flux, magnetic monopole, quantization etc. Additionally, magnetic monopole and electromagnetic angular momentum could be quantized by using semi-classical methods (Sakurai, 1994; Jackson, 1999). After the meaning of the gauge symmetry and calculation of vector potential, we disscus the scattering of charged particles on the selenoid (Dirac string), scattering amplitude and differantial cross section.

Keywords

• Aharonov-Bohm,Dirac Quantization,Gauge Transformations,Scattering,Monopole

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