Sferi chni garmo niki nabir ortonormovanih funkcij dvoh kutovih zminnih 8 displaystyle theta i f displaystyle varphi yaki skladayut povnij bazis funkcij sferichnogo kuta Vizualne zobrazhennya pershih dekilkoh sferichnih garmonik Chervonij kolir vkazuye na dodatnist funkciyi zelenij na vid yemnist Sferichni garmoniki poznachayutsya Y l m 8 f displaystyle Y l m theta varphi de l 0 1 2 a m probigaye znachennya vid l do l Y l m 8 f 1 m m 2 2 l 1 4 p l m l m P l m cos 8 e i m f textstyle Y l m theta varphi 1 m m 2 sqrt frac 2l 1 4 pi frac l m l m P l m cos theta e im varphi de P l m x displaystyle P l m x priyednani polinomi Lezhandra Sferichni garmoniki ye vlasnimi funkciyami operatora kutovogo momentu Mnozhnik v oznachenni sferichnih garmonik vibirayetsya z umovi normuvannya Y l m 8 f Y l m 8 f d W d l l d m m displaystyle int Y l prime m prime theta varphi Y l m theta varphi d Omega delta l l prime delta m m prime de integruvannya provoditsya po povnomu sferichnomu kutu a d l l displaystyle delta l l prime simvol Kronekera Deyaki sferichni garmoniki z malimi l RedaguvatiDokladnishe Spisok sferichnih garmonikY 0 0 8 f 1 2 1 p displaystyle Y 0 0 theta varphi 1 over 2 sqrt 1 over pi nbsp Y 1 1 8 f 1 2 3 2 p sin 8 e i f displaystyle Y 1 1 theta varphi 1 over 2 sqrt 3 over 2 pi sin theta e i varphi nbsp Y 1 0 8 f 1 2 3 p cos 8 displaystyle Y 1 0 theta varphi 1 over 2 sqrt 3 over pi cos theta nbsp Y 1 1 8 f 1 2 3 2 p sin 8 e i f displaystyle Y 1 1 theta varphi 1 over 2 sqrt 3 over 2 pi sin theta e i varphi nbsp Y 2 2 8 f 1 4 15 2 p sin 2 8 e 2 i f displaystyle Y 2 2 theta varphi 1 over 4 sqrt 15 over 2 pi sin 2 theta e 2i varphi nbsp Y 2 1 8 f 1 2 15 2 p sin 8 cos 8 e i f displaystyle Y 2 1 theta varphi 1 over 2 sqrt 15 over 2 pi sin theta cos theta e i varphi nbsp Y 2 0 8 f 1 4 5 p 3 cos 2 8 1 displaystyle Y 2 0 theta varphi 1 over 4 sqrt 5 over pi 3 cos 2 theta 1 nbsp Y 2 1 8 f 1 2 15 2 p sin 8 cos 8 e i f displaystyle Y 2 1 theta varphi 1 over 2 sqrt 15 over 2 pi sin theta cos theta e i varphi nbsp Y 2 2 8 f 1 4 15 2 p sin 2 8 e 2 i f displaystyle Y 2 2 theta varphi 1 over 4 sqrt 15 over 2 pi sin 2 theta e 2i varphi nbsp Posilannya RedaguvatiRozrahunok koeficiyentiv sferichnoyi garmoniki z kubichnoyi teksturi Pereglyanuto 15 zhovtnya 2014 Rozrahunok osvitlennya z dopomogoyu sferichnih garmonik v OpenGL Pereglyanuto 15 zhovtnya 2014 nbsp Ce nezavershena stattya z matematiki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Cya stattya potrebuye dodatkovih posilan na dzherela dlya polipshennya yiyi perevirnosti Bud laska dopomozhit udoskonaliti cyu stattyu dodavshi posilannya na nadijni avtoritetni dzherela Zvernitsya na storinku obgovorennya za poyasnennyami ta dopomozhit vipraviti nedoliki Material bez dzherel mozhe buti piddano sumnivu ta vilucheno serpen 2018 Otrimano z https uk wikipedia org w index php title Sferichni garmoniki amp oldid 37594999
