loadingPlease 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??2to be : ln2.:
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)=(4c/m)sin121qa,其中C是最近邻平面之间的力常量，M是一个原子的质量。 2The special signifcance of phonon wavevetors that lie on the zone.
boundary is developed from the formula ,we can obtain when q=0,w(q)=0,when q=??a,w(q)?(4c/m)
122) What is the long wave limit长波极限 and what result结果 we can get from this limit?
一维单原子链、一维双原子链中，q的取值都只在一定范围之内。（一维单 原
子链： , 一维双原子链： ），长波极限就是q
取值趋向于范 围边界时ω的情况。
研究的意义在于了解极限情况下格波振动频率的情况。
Or 1当qa<<1时，将cosqa展开并取得近似，可得cosqa?1-（qa)2.
2由此色散系度为w2?(c/m）q2a2表明在长波极限下，频率与波长成正比。
五、 Explanations for the contents of Chapter V.
1) What is the Debye model and Debye T3 law? What is the concept of Debye temperature?
Solution:1)Debye model is the low of the Max planck blackbody radiation solid equivalents.in the Debye model ,the allow model vectors smaller than the K
2) Debye T3 law is when T 《?，U=3?3NKBT4/5?3，that can obtain
12?4TTCv?NkB()?234NkB()3
5??hv6?2N33) Debye temperature can define ??()
kBV2) Please explain the physics menaning of Umklapp Processes:UP过程：
1Solution:To the thermal nesistivity of electrons,which have more important effect
three phonon processes isn’t k1?k2?k3,it is k1?k2?k3?G,G is reriprocal lattice vectors called
Umklapp processes .In the processes the energy is constant .The phonon vector ,in the first ,Brillouin zones
has physics menaning .The umklapp processes can let the phonon vector back to the first Brillouin zones.
六、 Derivation for the contents of Chapter VI
1) Please derive the formula of energy levels of free electrons in one dimension.请导出一维自由电子能级的公式
Solution:For
H?Hschrodinger equation H????,we can obtain
?2d2?H?-???H,where
2mdx2?H is the electron orbital energy . To infintle potential boundary conditions
?n(0)?0,?n(l)?0,
We can obtain ?n?Asin(obtain energy ?n
3) Please derive the the Hall coefficient of Hall effect.请导出霍尔效应的霍尔系数 Solution:To
2?1x),?n?L,where A is a constant,so that we can ?n2the state electric field steady state ,the time derivative is
e?zero ,then Vx=?Ex?wc?Vy,
mVy??eBe?e?is eyctotion frequency ,when Ey?wc?Vx,Vz??Ez,where wc?mcmm?Vy?0,
We can get Ey??wc?Ex??eB?Ex.And the Hall coffinient defined is mRH?EyjxB,we can used jx?nqVx?ne2?Ex/mto get RH??1. ne七、Explanation and the derivation for the contents of Chapter VII.
Please explain the origin of the energy gap, and write out the free electron bands for [111] direction of wavevector space.请解释能隙的起源，并写了[ 111 ]方向的波矢空间的自由电子带。 八、Deravation and the calculation for the contents of Chapter VIII第八章.
1) Starting from the definition of group velocity vg , please give the effect mass m* described by the energy band vs wavevector k. 从群速Vg的定义，请把影响质量m *的能带与波矢k描述
P135
3) Based on the concept of the effective mass质量, please write out the energy of an electron电子 near the low edge边缘 of the conduction传导 band and that of an electron near the top of the valance band,respectively.
P139基于有效质量概念，请写出能靠近导带低边和一个电子，在价带顶的电子，分别。
一、
1、【马德隆常数的物理意义】在一个晶体内，其中一个离子的总电势能，可表示为一个与它距离最近的另一个离子电势能的M倍，E=ME0，其中E0为两个离子的系统的电势能，M称为马德隆常数（Madelung?constant），其值与晶体结构有关。
2、【德拜温度】1912?年德拜提出以连续介质的弹性波来代表格波，将布喇菲晶格看作是各向同性的连续介质。有?1个纵波和?2?个独立的横波。? 温度愈低，德拜模型近似计算结果愈好；?温度很低，主要的只有长波格波的激发。
3、费米面：如果固体中有N个自由电子，按照泡利原理它们基态是由N个电子由低到高填充的N个量子态。N个电子在k空间填充半径为kF球，球内包含的状态数恰 好等于N。一般称这个球为费米球，kF为费米半径，球的表面为费米面。? 二、
1、证明：面心立方的原胞基矢：? ????
?????体心立方的原胞基矢为：???
一、
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1、爱因斯坦理论能够反映出Cv在低温时下降的基本趋势。......