桂林电子科技大学2018年《815固体物理》考研专业课真题试卷

桂林电子科技大学2018年考研专业课真题试卷

科目代码: 815 科目名称:固体物理

注意：答案必须全部写在考点提供的答题纸上，写在试题上无效；答案要标注题号，答题纸要填写姓名和考号，并标注页码与总页数；交卷时，将答题纸与试题一起装入原试卷袋，用我校提供的密封条密封并签名。

一、简要解释下列问题（每小题6分，共30分）

1. 第一布里渊区

2. 布洛赫定理

3. 德哈斯-范阿尔芬效应

4. 作为能带论基础的三个基本近似：绝热近似、单电子近似和周期场近似。

5. 费米面、费米能、费米速度。

二、（30分）已知某晶体中相邻原子之间的相互作用势可以表示为：

其中,,,都是大于零的常数。

（1）说明右式两项代表的物理意义并求出处于平衡状态时的原子间距。（2）证明此系统可以处于稳定平衡态的条件是。

（3）只考虑最近邻相互作用，写出由N个相同原子组成的该晶体的总相互作用能的表达式。

三、（30分）设有N个相同原子组成的一维原子链，原子间距为a，质量为m，

链长。

（1）在只考虑最近邻相互作用（待定力常数为）和简谐近似下，试证明其晶格振动波的色散关系为：

（2）根据周期性边界条件给出格波波矢的可能取值及有意义的取值范围。（3）推出其态密度的表达式并绘图表示。

四、（30分）二维简单正方晶格，晶格常数为，每个原胞有一个原子，每个原

子只有一个s态价电子，使用紧束缚近似，只计入近邻相互作用：

（1）求出s电子组成的s能带的函数。

第 1 页共 2 页

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