发布时间 : 星期三 文章关于固体物理往年试题更新完毕开始阅读47b5c2ba940590c69ec3d5bbfd0a79563c1ed4ce
卷 A 学期： 2011 至 2012 学年度 第 1 学
期
一、Fill in the blanks with the proper concepts and formula for the contents of Chapter I.
The volume体积 of a parallelepiped平行六面体 with axes轴 a?,a??
12,a3 is defined定义 by： ；
Please write out the five 2D Bravais lattices布拉维格子 as : 正方晶格、六角晶格、长方晶格、有心长方晶格和斜方晶格
The possible 14 primitive cells原胞 are : 简单三斜晶格、简单立方晶格、体心立方晶格、面心立方晶格、三角晶格、六角晶格、简单单斜晶格、底心单斜晶格、简单正交晶格、底心
正交晶格、体心正交晶格、面心正交晶格、简单四角晶格和体心四角晶格 For the plane whose intercepts are 4,2,3, the reciprocals倒数 are 1/4、1/2、1/3 ,the smallest three integers整数 having the same ratio比率 are 3、6、4 . The cube faces of a cubic crystal 立方晶体的立方体面are 二、 Expression and the calculation for the contents of Chapter II.
1）Please write out three vectors向量 of the reciprocal lattice倒格子: b???1,b2,b3.by using vectors
a?,a??12,a3。
b1=(2π)·(a2*a3)/(a1·(a2*a3)）???????????????????????
?b2=(2π)·(a3*a1)/(a1·(a2*a3)）?????????????????????????? b3=(2π)·(a1*a2)/(a1·(a2*a3））
2) Calculate计算 the volume of the primitive cell of fcc lattice面心立方晶格：
晶格基矢?a?a?i,?b?a?j,?c?a?k 体积V=a?.(b??c?)?a3
原胞基矢a?2(?j?k?),a?a???a??1?a2?2(k?i),a3?2(i?j) 体积???a?a?a31.(2?a3)?4
三、 Derivation for the contents of the contents of Chapter III.
Please derive out the van der Waals-London Interaction范德瓦尔斯伦敦相互作用 from the linear harmonic oscillators model.线性谐振子模型
解：作为一个模型，考虑两个值距为R的全同线性谐振子1和2，每个振子
; ;
带有一个正电荷（+e）和一个负电荷（-e），正负电荷之间的距离分别为X1和X2，粒子沿X轴振动，动量分别用R1和R2表示，力常量为C。在未受
12111222个数扰作用时，该系统的哈密顿量为：yl0?p1?CX1?p2?CX2
2m22m2令yl1表示两个振子之间的库伦相互作用能，核间坐标为R，于是有 在X1X2《R的近似下，将上式展开，使得到最低级近似表达式为
2e2X1X2yl1?? 3R通过简正模变换：Xs?11(X1?X2);Xa?(X1?X2) 2211（Xs?Xa);X2?(Xs?Xa) 22并解出X1和X2：X1?同时取yl1的近似形式，是系统的中哈密顿量对角化，可以得出这两种模式相联系的动量Ps和Pa,P1?则
总
哈
密
11（Ps?Pa),P2?(Ps?Pa) 22顿量可以写成
112e2112e2222yl?yl0?yl1?[Ps?(c?3)Xs]?【Pa?(c?3)Xa2]
2m2R2m2R可得来。。振子的两个频率为
12e212e212e222W=[(c?3)/m]?W0[1?(3)?(3）?...]
R2R8R其中，W0=（c/m)^(1/2)
1该系统的零点能量为?（Ws?Wa)由于存在相互作用，这个值比未。。的
2值2-1/2?W0低△V
112e22A△V=?（△Ws?△Wa)???W0.(3)??6)
28RR四、Expression and the explanation fr the contents of Chapter IV.
o
1) Please write out the dispersion relation 色散关系of ω(q) for two atoms原子 Per Primitive Basis每个原始依据 , and explain the physical meaning of the formula公式.. 五、 Concepts and the derivation for the contents of Chpater V.
1) What is the Debye model德拜模型 and Debye T3 lawT3法? What is the concept概念 of
Debye temperature?
2) Please derive the Density of State in Three Dimension三维状态密度. 六、Derivations for the contents of Chapter VI.
1) Please derive the formula公式 of energy levels of free electrons自由电子的能量水平 in one dimension维.
2) Please derive the the Hall coefficient 霍尔系数of Hall effect.
七、Explanation and derivation for the contents of Chapter VII.
Please explain the origin of the energy gap, and write out the free electron bands for [110] direction of wavevector space.
Solution:olthe origin of the energy gap is the two standing waves and pile up electors at different regions
and therefore the two waves have different values of the potential energy ,Ihtsis the origin of the energy gap.
2)the free electron bands for [110] direction of wavevetor space is Energy band Ga/2π ?（000） ?（kxky0) 1 000 0 kx?ky
2π）?k2y π/a)2 （kx?22,3 100,100 （222π/a)2 4,5,6,7 010,010,001,001 （28,9,10,11 110,101,110,101
110，101 12,13,14,15 110,101，16,17,18,19 011,011,011,011
八、Concepts and the explanation for the contents of Chapter VIII.
1) A hole acts in applied electric and magnetic fields as if it has a positive charge +e. The possible reasons in five steps are:
Solution：1）kh??ke,the electrons in the full band the total wave vector is zero:?k?0
（kh)???e(ke）.let the valerve band energy zero point in the conduction 2）?hband above
3）Vh?Ve,the velocity of the hole is equal to the velocity of the missing electron.
4）mh?me,the effective mass is inversely propertional to the crrvature
d2?/dk2,and for the hde band ,
this has the opposite sum to that for an electron in the valence band.
dk15)?h?e(E?VhXB),this come from the equation of motion
dtcdk1?e?-e(E?VhXB), dtc2) Please explian the physical meaning of energy-k relation of following three semiconductor materials半导体材料 .
卷 B
学期： 2011 至 2012 学年度 第 1 学期
一、Fill in the blanks with the proper data or concepts in Chapter I.
Solid state physics largely concerned主要关注: (1）crystals晶体 (2) electrons in crystals ; Atoms
density
密
度
：
na?1023atoms/cm3
ne?1028~29electrons/cm3 ；
Translation vector平移矢量： 3 translation vector vs a1、a2、a3 /
????T?u1a1?u2a2?u3a3 ；
The volume of a parallelepiped 平行六面体 ???with axes is： a1.(a2?a3) ；
The posibble five 2D Bravais lattice are : 正方晶格、六角晶格、长方晶格、有心长方晶
格
和
斜
方
晶
格 ; Seven lattice system are : 三斜、单斜、正交、立方、四角、六角和三角晶系 ;
For the plane whose intercepts are 3,1,2, the reciprocals are 1/3、1/1、1/2 , ,the smallest three
integers having the same ratio are （ 263 ） . The cube faces of a cubic crystal are （100）（010）( 001) (100)( 010)和（001） 二、Calculations for the contents of Chapter II.
a1,a2,a3??????1） Please write out three vector of the reciprocal lattice: b1,b2,b3.
a3?a1a?a，b2?2π，b3?2π12 a1(a2?a3）a1(a2?a3）a1(a2?a3）??2)Please verify验证 the relation: b ? 2 a j ?? ?. ijiπExplain:b1?23) Calculate the volume 体积of the primitive cell of bcc lattice：
三、Calculations and the concept explanation for the contents of Chapter III.
a2?a3