关于固体物理往年试题

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: 321,,b b b.by using vectors321,,a a a。

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k a c ,j a b ,i a a ===体积V=3).(a c b a =⨯ 原胞基矢)(2),(2),(2a 321j i a a i k a a k j a+=+=+= 体积4a )a a .(a 3321=⨯=Ω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 thelinear 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321,,a a a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 。

在未受个数扰作用时，该系统的哈密顿量为：22222121021212121y CX p m CX p m l +++= 令1y l 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R X X 《21的近似下，将上式展开，使得到最低级近似表达式为321212y RX X e l -≅ 通过简正模变换：)(21);(212121s X X X X X X a -≡+≡ 并解出X1和X2：)(21);2121a s a s X X X X X X -=+=（ 同时取1y l 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)(212),21Pa Ps P Pa Ps -≡+≡（ 则总哈密顿量可以写成])2(21m 21])2c (2121[y 2322232210Xa Re c Pa Xs R e Ps m yl yl l +++-+=+=【 可得来。

振子的两个频率为W=...]2(81)2(211[]/)2[(2323202132+-±≅±）Re R e W m R e c 其中，W0=（c/m)^(1/2) 该系统的零点能量为)s 21Wa W +（ 由于存在相互作用，这个值比未。

的值2-1/2V W 低△0△V=))2(81.0)a s 216232RA R e W W W -=-=+ △（△ 四、Expression and the explanation f or the contents of Chapter IV.1) Please write out the dispersion relation 色散关系of ω(q) for two atoms 原子 Per PrimitiveBasis 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 T 3 lawT3法? What is the concept 概念 ofDebye 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 inone 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 upelectors at different regionsand therefore the two waves have different values of the potentialenergy ,Ihtsis the originof the energy gap.2)the free electron bands for [110] direction of wavevetor space isEnergy band Ga/2π ∈（000） ∈（y x k k 0)1 000 0 22k y x k +2,3 100,100 2)/2a π（ y x 22k 2k +±π）（ 4,5,6,7 010,010,001,001 2)/2a π（ 8,9,10,11 110,101,110,10112,13,14,15 110,101011011，，16,17,18,19 110,101,110,011八、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 possiblereasons in five steps are:Solution ：1）,k e h k -=the electrons in the full band the total wave vector iszero:0k =∑2）.()k e h h）（k e ∈-=∈let the valerve band energy zero point in the conduction band above3）,h e V V =the velocity of the hole is equal to the velocity of the missingelectron.4）,m e h m =the effective mass is inversely propertional to the crrvature,/d 22dk εand for the hde band ,this has the opposite sum to that for an electron in the valence band. 5)),1(dk XB V cE e dt h h += this come from the equation of motion ),1(-dk e XB V cE e dt h += 2) Please explian the physical meaning of energy-k relation of following three semiconductormaterials 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 incrystals ;Atoms density 密度：323/10cm atoms n a =329~28/10cm electrons n e =； Translation vector 平移矢量： 3 translation vector vs a1、a2、a3 /332211u a u a u a T ++= ；The volume of a parallelepiped 平行六面体 with axes is ： )a a .(a 321⨯ ；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 threeintegers 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. 1） Please write out three vector of the reciprocal lattice: 321,,b b b . Explain:））π）321213321132321321(2(2b (2b a a a b a a a a a a ⨯=⨯=⨯=2)Please verify 验证 the relation: . 3) Calculate the volume 体积of the primitive cell of bcc lattice ：三、Calculations and the concept explanation for the contents of Chapter III. 321,,a a a ij j i a b πδ2=∙Please calculate the Madelung constant 马德龙常数 for the infinite 无限的 line of ions 离子 of alternating sign 交替的迹象 for the one-dimensional chain 一维链to be : :四、Expression and exlanations for the contents of Chapter IV.1) Please write out the 1D dispersion relation of ω(q), and explain the physical meaning of the formula..ω(q)=,21sin )/c 4(21qa m 其中C 是最近邻平面之间的力常量，M 是一个原子的质量。