????? ??? ?????????

??????? ????

???????	????? ?????
??? ??	?????
???? ????	???????? ??? ??? ? ????? ????????
???? ??	????? ????????
??????	${\displaystyle n_{i}={\frac {g_{i}}{\exp \left({\frac {E_{i}-\mu }{k_{\rm {B}}T}}\right)-1}}}$

????? - ????? ????? - ????? ???? ??????

????? ??? ????????? (Bose-Einstein Statistics) ?? ??? ?????? ???????? ??????? ?? ??????? ??????? ^{[1] [2] [3]} ????? ?????? ????? ??? ??? ????? = 0 ?? 1 ? ?????? ?????? ?? ?? ?? ???? ??? ???????? ??? ?????? ???? . ????? ????????? ??? ????? ???-????????. ??? ?????????? ??? ??? ??? ????? 1/2 ????? ???? ????? ?????-????? .

????? ?? ???? ???? ??? ???????? ${\displaystyle \langle n(E)\rangle }$ ???? ??? ??? ????? ??????? ?? ???? E ?? ???? ??????? ??????? ??? ???? ????? ????? T ???? ??????? ??????? : ??????? ?? ???????? .

?? ???? ??? ???? ???? ??? ??? ???????? ?????? ???????? ?????? ????? ????????? (????? ????????? ???? ????? 0 ?? Spin=1):

${\displaystyle \langle n(E)\rangle ={\frac {1}{e^{\beta (E-\mu )}-1}}}$

???:

μ ????? ?????????

${\displaystyle \beta }$ ????? ???? ${\displaystyle 1/(k_{B}T)}$

k _B ???? ????????

T ???? ??????? ????

?????? ????? ????????? (?? ?????? ????????? ) μ ??? ???? ???????.

?????? ???????? ??? ???????? ?? ?????? ???????? E? ????? ???? ??? ??? ???????? ????? ????? ?????? ?????. ???? ???? ?????? E ?????? (????? ???? ????????? ???? ) ???? ??? ???? ???????? g _i ?? ???????? ???????.

??? ???? ??????? ?????? ???????? ??? ${\displaystyle T_{\lambda }}$ ???? ??? ?????? ?????? ?? ??? ???? ???? ??? ????????? ?? ?????? ?? ????? ????????? μ ???? ?? ?????? ??????? ???? ??? ???? ???-????????.

??? ???? ????? ?????-????? ???? ??? ???????? ??????? ???? ???? ?????? ????? ?????? (+) ???? ?? ????? ??? ?????(-).

??:

${\displaystyle \langle n(E)\rangle ={\frac {1}{e^{\beta (E-\mu )}+1}}}$

???????? ?????????? ??? ???? ????? ?????-?????? ??? ????? ??? ??????? ??????? E ??? ????? ????????? ??? ????? ???? ????? ???-??????? ??? ??????? ??????? ??? ????? ????????. ???? ????? ???????? ???? ??? ????? ?????? ?? ???????? ?? ???? ???? ?? ???? ????? ?????.

????? ?????????? ?? ??? ??? ????? 1/2.

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