1、16 5 v Vol.16No.5 1997 M 5COLLEGE PHYSICS May.1997 nei Xn 8 孙长勇 李丽华 王继锁 ( =S , 252059) K 1 ? =apsnei Xn T dB) , n ?、K/ 、 = ?# Vr T. 1oM ei Xn ; ; s | O414.2 d9 10 T Xn 8B 0, n d9 d0 1 5.B) K dM f , ? n 5 #.D1) dM 0 ,9 B+ y f . ) B f /n bW ? =aps(s=1 M f ,s=2 dM f )ei Xn , ? n n ?、 、 = ?# BVr T.t s、n
2、 W1e .B 1 0 #D1T T+ . n5 ? =apsn1 0 RVr T.1 0 ? =aps=a(p21+p22+p2)s/2, n i=1 p2i= a 2/s n bWR o8 T2 Vn(R)= i x2iR2 d x1dx2dxn =CnR n , Cn= n/2 (n/2)! ? w = 0 V ? ()=ghn i p2i a 2/s dq1dq2dqndp1 dp2dpn =qhnV(n)cn a n/s TV(n)=dq1dq2dqnn 0 S,g1eiy0.#1 0 RVr T D()= () =ghnV(n)Cn ns a-nsns -1(1) e, 7m=ns
3、 ,bm=ghn V(n)Cnma-m (2) 5D()=bmm-1 (3) 1 n ?BVr T , Hn s f()= 1 ( 0) # 0 N = 0 0 D()d= 0 0 bm m-1d =bmm m0 ,Nn ? 0= mNbm 1/m (4) l :1995-11-21; :1996-08-22 | T(2) T(4) 0= Nh nam gV(n)Cn 1/ m =a Nh n gV(n) (n/2)! n/2 s/n (5) ? =apsn Xn 8n ?BVr T. 2 T0 H BVr T K/,d 0 N= 0 D()d e(-)+1= 0 bmm-1d e(-)+1
4、kT Hq/ n s I= 0 f()d e(-)+1= 0 f()d+ 2 6(kT) 2 f()+ (6) N = 0 bm m-1d+2 6(kT) 2bm(m-1)m-2 =bmmm 1+m(m-1) 2 6 kT 2 V = mNbm 1 m 1+m(m-1)2 6 kT 2 -1m (7) Z 7i09=,MB) .ii T(7) - n ?0, T(4),# =0 1- ns -1 2 6 kT 0 2 (8) n Xn BVr T. n 、sW Be1. 6 , V ?9F,9 V ?hlM,s n %.yN M % 0 bW 0 ? 1 . 3 T0 Hd = ? BVr T
5、 K/d = ? U= 0 D()d e(-)+1= 0 bmmd e(-)+1 T(6) U= bmm+1m+1+ 2 6(kT) 2bmmm-1 = bmm+1m+1 1+m(m+1) 2 6 kT 2 (9) | T(8) T(9),09 |,5 U= bmm+1m+10 1-(m-1) 2 6 kT 0 2 m+1 1+m(m+1) 2 6 kT 0 2 |B) U= bmm+1m+10 1+(m+1) 2 6 kT 0 2 T(4)bm =mN/m0 , Tim = n/s,K U=nNn+s0 1+ ns +1 2 6 kT 0 2 (10) Nn Xn = ?BVr T,# BV
6、r T CV = U T V=nNn +s ns +1 2k2T 30 =ns 2 3 Nk kT 0 (11) Vn, nW e11 . ? (s B.N, ns ,CV T 1, 0 Xj 8CVTn/s1. yN 0d9n %T, PMM. T V9 ? =aps i Xn 80、UCV. , T0 HT kT H , 、 v Xn 8( 10 ),Y i z f . 16v 16 4 0 4.1 dM 10 (=p2/2m0) g=2,a=1/2m0,s=2. f , n =3, V(3)=V, T(5)、 (8)、(11)n ?、 sY 0= 12m0 Nh3 2V 3 2 1 2
7、3/2 2 3 =h 2 2m0 3N 8V 2 3, =0 1- 2 12 kT 0 2 ,CV= 2 2 Nk kT 0 T3,4. = f ,n =2, V(2)=A( ),B Vr T 0= 12m 0 Nh2 2A = Nh2 4m0 A =0,CV= 2 3 Nk kT 0 = H . T (6)7T. L= = f /,m = n/s=1. T(3)、(4), HD()=bm = N/0,# N = 0 bmd e(-)+1= N 0 kTln(1+e ) N =kTln(e0/kT-1) S T.kT 0 H 5 =0 (12) B f ,n =1, V(1)=L.# 0= 1
8、2m0 Nh2L12 2 = N 2h2 32m0L2 =0 1+ 2 12 kT 0 2 ,CV= 2 6 Nk kT 0 B0 679v, f . 4.2 M 10 (=cp) g=2,a=c,s=1. f ,n=3. T(5)、(8)、(11) 0=c Nh 3 2V 3 /4 3/2 1 3 =hc 3N8V 1 3 =0 1- 2 3 kT 0 2 ,CV=2Nk kT0 = H,n=2 0=c Nh 2 2A 1 1 2=hc N 2A 1 2 =0 1- 2 6 kT 0 2 ,CV=2 2 3 Nk kT 0 B H,n=1 0=Nhc/4L =0,N T(12) . CV=
9、2 3 Nk kT 0 . 5 ID 1 f ,Z.0 M.v ,1995,14(1):18 2 , , . d9 .: ,1980.335 3 . d9 .2.: ,1993 4 .d9 . Z:v ,1990 CHEMICAL POTENTIAL AND HEAT CAPACITY OF n-DIMENSIONAL DEGENERATE FEIMIGAS Sun Changyong Li Lihua Wang Jisuo (Department of Physics, Liaocheng TeachersCollege, Liaocheng, Shandong, 252059, China) Abstract The n -dimensional degenerateFermi gases which have energy spectrum of =aps arediscussed.Theexpressionsof Fermienergy, chemicalpotential and heat capacity of thegases are given. Keywords degenerateFermigas;chemical potential;heat capacity 175 :nei Xn 8
