In quantum mechanics, the results of the quantum particle in a box can be used to look at the equilibrium situation for a quantum ideal gas in a box which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation (photon gas) which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass.
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| rdfs:label
| - Gas in a box (en)
- 箱の中の気体 (ja)
- Gás em uma caixa (pt)
- 盒中氣體 (zh)
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| rdfs:comment
| - 本項では、量子力学における箱の中の量子的な理想気体について述べる。すなわち、容器に多数の分子が入っており、熱化のプロセスで一瞬に行われる衝突を除けば、分子どうしの相互作用を行わない系である。この系の平衡状態における性質を調べるには、無限の深さの井戸型ポテンシャルに置かれた量子的粒子についての結果を用いることができる。 この単純なモデルは、質量をもつ理想フェルミ気体や、質量を持つ理想ボース気体、質量をもたないボース気体として扱うことが可能な黒体放射などの様々な量子理想気体だけでなく、古典的な理想気体も記述することができる。黒体放射における熱化は、フォトンおよび熱平衡状態にある物体との間の相互作用により促進されると仮定される。 マクスウェル＝ボルツマン統計またはボース＝アインシュタイン統計またはフェルミ＝ディラック統計の結果を用い、箱の大きさが無限大だとすると、トーマス＝フェルミ近似によりエネルギー状態の縮退度は微分として、状態の総和は積分として表現される。これにより気体の熱力学的な性質は分配関数やグランドカノニカル分配関数を用いて計算できる。ここではいくつかの簡単な例を示す。 (ja)
- 在量子力學裏，盒中氣體（Gas in a box）是一个理论模型，指的是在一個盒子內，一群不會互相作用的粒子。盒子內的位勢為零，盒子外的位勢為無限大。這些粒子永遠地束縛於盒子內，無法逃出。靠著粒子與粒子之間數不盡的瞬時碰撞，盒中氣體得以保持熱力平衡狀況。盒中氣體這個簡單的理論模型可以用來描述經典理想氣體，也可以用來描述各種各樣的量子理想氣體，像費米氣體、玻色氣體、黑體輻射、等等。 應用馬克士威-玻茲曼統計、玻色-愛因斯坦統計、與費米-狄拉克統計的理論結果，取非常大的盒子的極限，表達能量態的簡併為一個微分，然後以積分來總合每一個能量態，再用配分函數或計算氣體的熱力性質。這計算的結果可以用來分析正質量粒子氣體或零質量粒子氣體的性質。 此篇文章是盒中粒子理論的進階。閱讀此篇文章前，必須先了解盒中粒子理論。 (zh)
- In quantum mechanics, the results of the quantum particle in a box can be used to look at the equilibrium situation for a quantum ideal gas in a box which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation (photon gas) which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass. (en)
- Em mecânica quântica, os resultados de uma partícula quântica em uma caixa podem ser usados para visualizar-se a situação de equilíbrio para para um ideal em uma caixa na qual está contido um grande número de moléculas as quais não interegem com outras exceto por colisões térmicas instantâneas. Este modelo simples pode ser usado para descrever um gás clássico ideal tanto quanto um gás de Fermi ideal massivo, o gás de Bose ideal massivo tão bem quanto uma radiação de corpo negro a qual pode ser tratada como um gás de Bose desprovido de massa. (pt)
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| - In quantum mechanics, the results of the quantum particle in a box can be used to look at the equilibrium situation for a quantum ideal gas in a box which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation (photon gas) which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass. Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics, and considering the limit of a very large box, the Thomas–Fermi approximation (named after Enrico Fermi and Llewellyn Thomas) is used to express the degeneracy of the energy states as a differential, and summations over states as integrals. This enables thermodynamic properties of the gas to be calculated with the use of the partition function or the grand partition function. These results will be applied to both massive and massless particles. More complete calculations will be left to separate articles, but some simple examples will be given in this article. (en)
- 本項では、量子力学における箱の中の量子的な理想気体について述べる。すなわち、容器に多数の分子が入っており、熱化のプロセスで一瞬に行われる衝突を除けば、分子どうしの相互作用を行わない系である。この系の平衡状態における性質を調べるには、無限の深さの井戸型ポテンシャルに置かれた量子的粒子についての結果を用いることができる。 この単純なモデルは、質量をもつ理想フェルミ気体や、質量を持つ理想ボース気体、質量をもたないボース気体として扱うことが可能な黒体放射などの様々な量子理想気体だけでなく、古典的な理想気体も記述することができる。黒体放射における熱化は、フォトンおよび熱平衡状態にある物体との間の相互作用により促進されると仮定される。 マクスウェル＝ボルツマン統計またはボース＝アインシュタイン統計またはフェルミ＝ディラック統計の結果を用い、箱の大きさが無限大だとすると、トーマス＝フェルミ近似によりエネルギー状態の縮退度は微分として、状態の総和は積分として表現される。これにより気体の熱力学的な性質は分配関数やグランドカノニカル分配関数を用いて計算できる。ここではいくつかの簡単な例を示す。 (ja)
- Em mecânica quântica, os resultados de uma partícula quântica em uma caixa podem ser usados para visualizar-se a situação de equilíbrio para para um ideal em uma caixa na qual está contido um grande número de moléculas as quais não interegem com outras exceto por colisões térmicas instantâneas. Este modelo simples pode ser usado para descrever um gás clássico ideal tanto quanto um gás de Fermi ideal massivo, o gás de Bose ideal massivo tão bem quanto uma radiação de corpo negro a qual pode ser tratada como um gás de Bose desprovido de massa. Usando os resultados de qualquer uma das da , estatística de Bose-Einstein ou estatística de Fermi-Dirac nós usamos a e levamos ao limite de uma caixa muito grande, e expressamos a degeneração dos estados de energia como um diferencial, e somatórios sobre os estados como integrais. Nós iremos então estar em posição de calcular as propriedades termodinâmicas do gás usando a função partição ou a grande função partição. Estes resultados serão obtidos tanto para as partículas massivas quanto para as desprovidas de massa. (pt)
- 在量子力學裏，盒中氣體（Gas in a box）是一个理论模型，指的是在一個盒子內，一群不會互相作用的粒子。盒子內的位勢為零，盒子外的位勢為無限大。這些粒子永遠地束縛於盒子內，無法逃出。靠著粒子與粒子之間數不盡的瞬時碰撞，盒中氣體得以保持熱力平衡狀況。盒中氣體這個簡單的理論模型可以用來描述經典理想氣體，也可以用來描述各種各樣的量子理想氣體，像費米氣體、玻色氣體、黑體輻射、等等。 應用馬克士威-玻茲曼統計、玻色-愛因斯坦統計、與費米-狄拉克統計的理論結果，取非常大的盒子的極限，表達能量態的簡併為一個微分，然後以積分來總合每一個能量態，再用配分函數或計算氣體的熱力性質。這計算的結果可以用來分析正質量粒子氣體或零質量粒子氣體的性質。 此篇文章是盒中粒子理論的進階。閱讀此篇文章前，必須先了解盒中粒子理論。 (zh)
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