ࡱ> G9( / 0DTimes New Roman0z[ 0D[SOes New Roman0z[ 0 DNSeeO New Roman0z[ 00DwiSO_GB2312Roman0z[ 01@DfNGB2312Roman0z[ 01PDўSOGB2312Roman0z[ 0`DSymbol12Roman0z[ 0@ .  @n?" dd@  @@`` @8Tk     W  0AA ff3f33f@fC ʚ;3ʚ;g4<d<d z[ 0ppp@ <4!d!dL 0<4ddddL 0<4BdBdL 0 80___PPT10 ZZ? %2&ϑP[~l BoltzmannR^_H}'<f '<f'<f  4. ϑP[~l 6qLuv_‰|P[R:N$N'Y{|: srP[(Bose particle): Nu[O)R Nv[St; 9s|P[(Fermi particle): u[O)R Nv[St. N0Bose-Einstein~ BoseP[N*NϑP[`S[~Y*N|P[. [‰SO|vpRf[s^a`b gpevgvQ]'Yv_‰ЏRr`0ُN_‰ЏRr`X[(WNTy N TvR^-N0 R^(WnSO|[‰agN(YU0V0TI{)vMRc N |P[(WT~ NvRMe_0b&(! &,f!@ & f$f f$f$! $ /$$$!($(,$,!0&0$4$4!8$8<$<!$$!$ $ !   <D (WTR^-N, _X[(WNyR^b gv_‰r`pegY, dkR^QsvQsg'Y, y:NgSQR^. SNfgSQR^v|P[(W~ NvR^lQ_: Ni* = gi /(e+"i 1) (3) b=1/kT 1ui Ni=NBlQ0 N0Fermi Dirac~ 9s|P[u[O)R Nv[St, k*NϑP[`S[~N*N|P[. gY NR^: {Ni} "0RRR"iRRR N0 RRR NiRRR n iNi = N iNi"i= E #)!&!      !  $ +!! !!!!!!!!!!!!!!!!!!!N   CHQBl~ivM[peWi: Wi = CgiNi = gi! /Ni!(gi Ni)! R^{Ni} b gvr`peW:N: W = Pi [gi! /Ni!(gi Ni)!] (4) SO|b gv_‰r`pe/fTyR^KNT: =W=S[Pi [gi! /Ni!(gi Ni)!]] (5) 9s|P[vgSQR^1u N_h:y Ni = gi /(e+"i +1) (6) =1/kT; 1uNi = NSBlQ.:Z &.& $!,!$!,!,!$!,!$!,!$!,!$!,!$!&. & $!$,$,$,$,$, $&$!$$,$,$,$,$, $&$!$,$,$,$$! &.&h  $ |BlgSQR^ W ="i (gi Ni / Ni!) lnW="i(Nilngi NilnNi + Ni) (10) N: f =lnW="i(Ni lngi NilnNi + Ni) (11) y1 = "i Ni Ni = 0 (12) y2 = "i Ni"i E = 0 (13) b?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> n(    6PR P  :USQdkYkHrh7h_   08T   r8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~   0 Z ``  X*  0X `   Z*  0ʡ `   Z*T  <d޽h ? ̙33  ؞!jg  P(  Pr P S 06    H P 0޽h ? ̙33___PPT10i.ۓpM+D=' = @B +<  LD  (     c $¡P <$  0  H  0޽h ? ̙33___PPT10p.+ouD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D4' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* >%(D' =-m6Bbox(in)*<3<* >D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* >^%(D' =-m6Bbox(in)*<3<* >^D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ^q%(D' =-m6Bbox(in)*<3<* ^qD' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* q%(D' =-m6Bbox(in)*<3<* qD' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* +8+0+  +t D(  DN D S pQ%<$ 0 0 SO|+TN*NsrP[, vQ(W~ NvNyR^/f:[Ni\ ~ "0, "1, & , "i & |P[pe N0, N1, & , Ni & agN "i Ni"i = E; "i Ni = N WR^[Ni\wQ gv_‰ЏRr`pev. HQBlgN~v N T_‰r`pe(sSM[pe): : ~vϑ "i ~v{v^^: gi ~v|P[pe: Ni :<5$!,! $!,!$!,!$!,!$!,!$!,!$!,! $!,!$!,!$!,!$!,!$!,!$!,!$! $f,f$f,f$f,f $f,f$f,f$f$!,!$!%f %!-!%!-!%!-!%!-!%!!$   H D 0޽h ? ̙33&___PPT10.At+] )D' = @B DU' = @BA?%,( < +O%,( < +D' =%(D:' =%(DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D7%(D' =-u6Bdiamond(in)*<3<*D7DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D7V%(D' =-u6Bdiamond(in)*<3<*D7VDF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*DV|%(D' =-u6Bdiamond(in)*<3<*DV|D' =%(D' =%(DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D|%(D' =-u6Bdiamond(in)*<3<*D|D' =%(D' =%(DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-u6Bdiamond(in)*<3<*DD' =%(D' =%(DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-u6Bdiamond(in)*<3<*D+8+0+D0 +    0 | (    S Q,Z<$  0 Q dkr`pevBl{/fNcR~T: qQ ggi + Ni*Ne }, YVcR, eFhNhϑP[`, Wth:y_‰|P[, eFhTbv\tGWYNdkeFh@bNhvϑP[` P$!$f,f$f,f $f$$f$$f$!$2  6Qw1 ,$ 0 D % 0 % % 0 0 % % 0 0 0 % & & # #(! l kP   kP ,$D 0  0bQk P   gi y b8 2f fffB  6Dffo l * c~ * c~,$D  0l   <ff>* P    <Qfo c~ .~vM[pe:N:gi(gi + Ni 1)!' $$$$$$$8l &   &  ,$D 0l   <ffԔ&     B?Q /  (gi+Ni 1)!y b 2f.H  0޽h ? ̙33___PPT10.+l8vuD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B%strips(downRight)*<3<*PD' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B+checkerboard(across)*<3<* D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DE' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%strips(downRight)*<3<*+p+0+Q ++0+Q + '   @J (     c $p6%<$  0 Q z ϑP[`T|P[MOnvNbc NONuev`, Ee^[|P[vhQ T'`TϑP[`vMOnesQ'`ۏLOck: Wi = gi(gi + Ni 1)! /(gi)!(Ni)! = gi(gi + Ni 1)! / gi(gi 1)!(Ni)! = (gi + Ni 1)! / (Ni)!(gi 1)! R^[Ni\b gvϑP[`pe:N: W = PiWi = Pi[(gi+Ni 1)! / Ni!(gi-1)!] (1) SO|b gvϑP[`pe:NTyR^ϑP[`peKNT: = W =S[Pi (gi+Ni-1)! / Ni!(gi-1)!] (2) Ni=N Ni"i=E b&!&&!.!&!.!&!.!&!.!&!.!&!.!&!&.&!.!&!.!&!&.&!.!&!.!&!.!&!.! &!.!&!.!&!  !       !$$$$$$$$$$$$$$  H  0޽h ? ̙33___PPT10.+!fDr' = @B D-' = @BA?%,( < +O%,( < +D' =%(DR' =%(DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-P%(D' =-}6B!strips(upRight)*<3<*-PDN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P~%(D' =-}6B!strips(upRight)*<3<*P~DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*~%(D' =-}6B!strips(upRight)*<3<*~DT' =%(D' =%(DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!strips(upRight)*<3<*DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!strips(upRight)*<3<*DV ' =%(D ' =%(DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!strips(upRight)*<3<*DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!strips(upRight)*<3<*DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =-}6B!strips(upRight)*<3<*2DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2D%(D' =-}6B!strips(upRight)*<3<*2DDN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Db%(D' =-}6B!strips(upRight)*<3<*Db+8+0+Q +z  LDp(    c $(#QW<$ 0 Q H  0޽h ? ̙33___PPT10.+BKDN' = @B D ' = @BA?%,( < +O%,( < +D8' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ge%(D' =-o6Bdissolve*<3<*GeD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*e}%(D' =-o6Bdissolve*<3<*e}D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*~%(D' =-o6Bdissolve*<3<*~D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(D ' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =-o6Bdissolve*<3<*#+8+0+ +  LD(    c $`L <$ 0  H  0޽h ? ̙33NF___PPT10&.+}$qD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =-6B+checkerboard(across)*<3<*5Dh' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*6G%(D' =-6B+checkerboard(across)*<3<*6GDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*Gq%(D' =-6B+checkerboard(across)*<3<*GqDh' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*r%(D' =-6B+checkerboard(across)*<3<*rDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*D' =%(Dp' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*+8+0+ +p.   P  (   b   c $h;(<$  0 6   N0Boltzmann~ S_gi >> NieBose-Einstein~ Fermi-Dirac ~ N TNgP ~vϑP[`pe: 5"gi >>Ni gi >>1 4"Ni+ gi 1H"gi Wi = (gi + Ni 1)!/Ni!(gi 1)! = (gi + Ni 1)(gi + Ni 2)& gi (gi-1)! / Ni!(gi-1)! = gi gi & gi / Ni! = gi Ni / Ni! (7) R^{Ni} vϑP[`peI{N~ϑP[`pevXNy: W ="i (gi Ni / Ni!) (8) SO|b gvy_‰ЏRr`pe:N: = W (Ni=N; Nii=E) (9)& &.&.C&&   !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !  !        !  !  !         !  !  !  !  !  !  !  !  !  !  !  !  !  !   !'/'!     '!       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