# 玻尔兹曼分布

${\displaystyle F({\rm {state}})\propto e^{-{\frac {E}{kT}}}}$

${\displaystyle {\frac {F({\rm {state2}})}{F({\rm {state1}})}}=e^{\frac {E_{1}-E_{2}}{kT}}}$

## 分布形式

${\displaystyle p_{i}={\frac {e^{-{\varepsilon }_{i}/kT}}{\sum _{j=1}^{M}{e^{-{\varepsilon }_{j}/kT}}}}}$

${\displaystyle Q={\sum _{i=1}^{M}{e^{-{\varepsilon }_{i}/kT}}}}$

${\displaystyle p_{i}={\frac {1}{Q}}{e^{-{\varepsilon }_{i}/kT}}}$

${\displaystyle {\frac {p_{i}}{p_{j}}}=e^{({\varepsilon }_{j}-{\varepsilon }_{i})/kT}}$

${\displaystyle p_{i}={\frac {N_{i}}{N}}}$

${\displaystyle {\frac {N_{i}}{N}}={\frac {e^{-{\varepsilon }_{i}/kT}}{\sum _{j=1}^{M}{e^{-{\varepsilon }_{j}/kT}}}}}$

## 參考文獻

1. ^ Landau, Lev Davidovich & Lifshitz, Evgeny Mikhailovich. Statistical Physics. Course of Theoretical Physics 5 3. Oxford: Pergamon Press. 1980 [1976]. ISBN 0-7506-3372-7. Translated by J.B. Sykes and M.J. Kearsley. See section 28
2. McQuarrie, A. (2000) Statistical Mechanics, University Science Books, California
3. Atkins, P. W. (2010) Quanta, W. H. Freeman and Company, New York
4. ^
5. ^ NIST Atomic Spectra Database Levels Form页面存档备份，存于互联网档案馆） at nist.gov
6. ^ Atkins, P. W.; de Paula J. (2009) Physical Chemistry, 9th edition, Oxford University Press, Oxford, UK
7. ^ Skoog, D. A.; Holler, F. J.; Crouch, S. R. (2006) Principles of Instrumental Analysis, Brooks/Cole, Boston, MA