Density of states

In classical mechanical systems, the points in phase space (γ-space) represent the microscopic (mechanical) states of the system. The number of states whose energy is within a small interval Δ E around E is given by

g ( E ) ΔE
This g ( E ) is called the density of states. For example, when a particle of mass m is contained in a container of volume V ,

( h is Planck's constant). In quantum mechanical systems, the density of states also coincides with g ( E ) mentioned above if the energy levels are distributed over a sufficiently small width. The density of states of a system consisting of many particles is expressed as entropy S ( E ), which is a thermodynamic quantity.

1/ g ( E ) ∝ exp{− S ( E )/ k }
There is a universal relationship between the quantities (which do not include quantities that indicate the properties of the system being treated).

Source: Morikita Publishing "Chemical Dictionary (2nd Edition)" Information about the Chemical Dictionary 2nd Edition

古典力学的な系では，位相空間(γ-空間)の点は系の微視的(力学的)状態を表す．体系のエネルギーがEのまわりの小区間ΔE内にある状態の数は

g(E)ΔE
と表現することができ，このg(E)を状態密度という．たとえば，質量mの粒子が体積Vの容器に入っているとき，

と与えられる(hはプランク定数)．量子力学的な系においても状態密度は，エネルギー準位が十分小さい幅で分布している場合には前述のg(E)と一致する．多数の粒子からなる系の状態密度は熱力学的量の一つであるエントロピーS(E)と

1/g(E) ∝ exp{－S(E)/k}
なる普遍的な関係をもっている(扱う系の性質を示す量を含まない)．

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