设体系的粒子有两个非简并能级:ε1=0 ε2=ε.如果体系允许最多有两个全同粒子 求体系的巨配分函数 平均粒子数

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设体系的粒子有两个非简并能级:ε1=0,ε2=ε.如果体系允许最多有两个全同粒子,求体系的巨配分函数、平均粒子数和每个能级的粒子平均占有数.

热搜:仅具有置0和置1功能的触发器是

答案解析

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  • 令N1,N2分别为单粒子能级1和能级2上的占有数,则体系的粒子数
       N=N1+N2,    (1)
       体系的能量为
       E=N2ε=(N-N1)ε.    (2)
       (1)如果体系的粒子是费米子,体系的巨配分函数则为
       latex.action?latex=XFhpID1cc3VtIF97Tj0wfV57Mn1lXnstXGFscGhhIE59XHN1bSBfe0V9ZV57LVxmcmFje0V9e2tU%0D%0AfX09MStlXntcZnJhY3tcbXUgfXtrVH19XGxlZnQoIDErZV57LVxmcmFje1x2YXJlcHNpbG9uIH17%0D%0Aa1R9fVxyaWdodCkrZV57XGZyYWN7MlxtdSAtXHZhcmVwc2lsb24gfXtrVH19PVxsZWZ0KCAxK2Ve%0D%0Ae1xmcmFje1xtdSB9e2tUfX1ccmlnaHQpXGxlZnQoIDErZV57XGZyYWN7XG11IC1cdmFyZXBzaWxv%0D%0AbiB9e2tUfX1ccmlnaHQp,(3)
       式中,latex.action?latex=ZV57LVxhbHBoYSB9PWVee1xmcmFje1xtdX17a1R9fQ%3D%3D气体的逸度,μ为气体的化学势,k为玻尔兹曼常量.体系具有粒子数N和能量E的概率为
       latex.action?latex=UFxsZWZ0KCBOLEVccmlnaHQpPVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7TlxtdSAtRX17a1R9fQ%3D%3D.    (4)
       体系的平均粒子数为
       latex.action?latex=XGJhciB7Tn09XHN1bSBfe049MX1eezJ9TlxzdW0gX3tFfVBcbGVmdCggTixFXHJpZ2h0KQ%3D%3D
       latex.action?latex=PVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7XG11IH17a1R9fVxsZWZ0KCAxK2Veey1cZnJhY3tcdmFy%0D%0AZXBzaWxvbiB9e2tUfX1ccmlnaHQpK1xmcmFjezJ9e1xYaSB9ZV57XGZyYWN7MlxtdSAtXHZhcmVw%0D%0Ac2lsb24gfXtrVH19
       latex.action?latex=PVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7XG11IH17a1R9fVxsZWZ0KCAxK2Vee1xmcmFje1xtdSAt%0D%0AXHZhcmVwc2lsb24gfXtrVH19XHJpZ2h0KStcZnJhY3sxfXtcWGkgfVxsZWZ0KCBlXntcZnJhY3tc%0D%0AbXUgLVx2YXJlcHNpbG9uIH17a1R9fStlXntcZnJhY3syXG11IC1cdmFyZXBzaWxvbiB9e2tUfX1c%0D%0AcmlnaHQp
       latex.action?latex=PVxmcmFjezF9e2Vee1xmcmFjey1cbXUgfXtrVH0rMX19Kz1cZnJhY3sxfXtlXntcZnJhY3tcdmFy%0D%0AZXBzaWxvbiAtXG11IH17a1R9KzF9fQ%3D%3D.  (5)
       能级1上,粒子占有数的平均值为
       latex.action?latex=XGJhciB7Tl97MX19PVxzdW0gX3tOPTF9XnsyfVxzdW0gX3tFfU5fezF9UChOLEUp
       latex.action?latex=PVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7XG11IH17a1R9fVxsZWZ0KCAxK2Vee1xmcmFje1xtdSAt%0D%0AXHZhcmVwc2lsb24gfXtrVH19XHJpZ2h0KQ%3D%3D
       latex.action?latex=PVxmcmFjezF9e2Veey1cZnJhY3tcbXUgfXtrVH19KzF9.  (6)
       能级2上,粒子占有数的平均值为
       latex.action?latex=XGJhciB7Tl97Mn19PVxzdW0gX3tOPTF9XnsyfVxzdW0gX3tFfU5fezJ9UFxsZWZ0KCBOLEVccmln%0D%0AaHQpPVxmcmFjezF9e1xYaSB9XGxlZnQoIGVee1xmcmFje1xtdSAtXHZhcmVwc2lsb24gfXtrVH19%0D%0AK2Vee1xmcmFjezJcbXUgLVx2YXJlcHNpbG9uIH17a1R9fVxyaWdodCk9XGZyYWN7MX17ZV57XGZy%0D%0AYWN7XHZhcmVwc2lsb24gLVxtdSB9e2tUfX0rMX0%3D.  (7)
       (2)如果体系的粒子是玻色子,体系的巨配分函数可写为
       latex.action?latex=XFhpID1cc3VtIF97Tj0wfV57Mn1lXntcZnJhY3tOXG11fXtrVH19XHN1bSBfe05fezJ9PTB9XntO%0D%0AfWVeey1cZnJhY3tFfXtrVH19
       latex.action?latex=PTErZV57XGZyYWN7XG11fXtrVH19XGxlZnQoIDErZV57LVxmcmFje1x2YXJlcHNpbG9uIH17a1R9%0D%0AfVxyaWdodCkrZV57XGZyYWN7MlxtdSB9e2tUfX1cbGVmdCggMStlXntcZnJhY3stXHZhcmVwc2ls%0D%0Ab24gfXtrVH19K2Veey1cZnJhY3syXHZhcmVwc2lsb24gfXtrVH19XHJpZ2h0KQ%3D%3D.  (8)
       体系的平均粒子数为
       latex.action?latex=XGJhciB7Tn09XHN1bSBfe049MX1eezJ9XHN1bSBfe05fezJ9PTB9XntOfU5QXGxlZnQoIE4sRVxy%0D%0AaWdodCk%3D
       latex.action?latex=PVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7XG11fXtrVH19XGxlZnQoIDErZV57LVxmcmFje1x2YXJl%0D%0AcHNpbG9uIH17a1R9fVxyaWdodCkrXGZyYWN7Mn17XFhpIH1lXntcZnJhY3syXG11IH17a1R9fVxs%0D%0AZWZ0KCAxK2Vee1xmcmFjey1cdmFyZXBzaWxvbiB9e2tUfX0rZV57LVxmcmFjezJcdmFyZXBzaWxv%0D%0AbiB9e2tUfX1ccmlnaHQp.  (9)
       能级1上,粒子占有数的平均值为
       latex.action?latex=XGJhciB7Tl97MX19PVxzdW0gX3tOPTF9XnsyfVxzdW0gX3tOX3sxfT0xfV57Tn1OX3sxfVBcbGVm%0D%0AdCggTixFXHJpZ2h0KQ%3D%3D
       latex.action?latex=PVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7XG11fXtrVH19XGxlZnQoIDErMmVee1xmcmFje1xtdSB9%0D%0Ae2tUfX0rZV57XGZyYWN7XG11IC1cdmFyZXBzaWxvbiB9e2tUfX1ccmlnaHQp.  (10)
       能级2上,粒子占有数的平均值为
       latex.action?latex=XGJhciB7Tl97MX19PVxzdW0gX3tOPTF9XnsyfVxzdW0gX3tOX3syfT0xfV57Tn1OX3syfVBcbGVm%0D%0AdCggTixFXHJpZ2h0KQ%3D%3D
       latex.action?latex=PVxmcmFjezF9e1xYaSB9ZV57XGZyYWN7XG11LVx2YXJlcHNpbG9uIH17a1R9fVxsZWZ0KCAxK2Ve%0D%0Ae1xmcmFje1xtdSB9e2tUfX0rMmVee1xmcmFje1xtdSAtXHZhcmVwc2lsb24gfXtrVH19XHJpZ2h0%0D%0AKQ%3D%3D.   (11)