ERHAN AKIN, Atilla GÜLEÇ, Hüseyin YÜKSEL

Küresel harmoniklerin tekrarlama bağıntıları ile hesaplanması

Bu çalışmada atomik ve moleküler hesaplamalarda yaygın olarak kullanılan küresel harmoniklerin istenilen bir $ell_{max}$ değerine kadar mümkün olan tüm $ell$ ve m kuantum sayı çiftleri için sayısal değerlerini veren bir tekrarlama bağıntısı elde. edilmiştir. Elde edilen bu tekrarlama bağıntısının, çok büyük kuantum sayıları ve tüm açı değerlerinde duyarlı sonuçlar verdiği bilgisayar hesaplamaları ile doğrulanmıştır.

Recursive relations of the spherical harmonics and their calculations

In this study a recursive relation was obtained for the spherical harmonics which is widely used in atomic and molecular calculations. The recursive relation gives the values of spherical harmonics for all possible combinations of quantum numbers $ell$ and m up to an arbitrary $ell_{max}$ value. It was also verified that this recursive relation gives accurate results for very large quantum number combinations and for all angles.

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