-石英晶体和铜块间手性不对称宏观力的研究

胡永红，靳海芹，毛彩霞

(1.湖北科技学院核技术与化学生物学院，湖北 咸宁 437100,2.湖北第二师范学院物理与电子信息学院，湖北 武汉 430205)

0 引言

1 手性宏观势

轴子在核子和电子间传递的相互作用有效势为:

(1)

图1-石英和吸引质量铜块的几何构形示意图

(2)

(3)

r〈Ψ|V(r)|Ψ〉r=r〈Ψ|P-1PV(r)P-1P|Ψ〉r=l〈Ψ|PV(r)P-1|Ψ〉l=-l〈Ψ|V(r)|Ψ〉l

(4)

根据如下的位置矢量变换：Prkj(r)P-1=-rkj,自旋的变换PσkP-1=σk和磁场的变换PBP-1=B.方程(3)对应(2)式势的不同手性，取相反的符号.

(5)

上式中的矩阵元乘积可以采用单电子近似简化.利用等式:(σi·A)(σj·B)=A·B+iσi·(A×B)对电子自旋求和，矩阵元可以重写为：

(6)

其中，|Ψk0〉和|Ψkn〉分别描述第i个原胞中第k个电子的初态和末态.

2 矩阵元乘积的讨论

(7)

{α|τ}Ψn(k1,r)=Ψn(αk1,r+τ)=eαk1·(r+τ)un(αk1,r+τ)=eαk1·rΨn(αk1,r)

(8)

3 结论分析及讨论

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