-石英晶體和銅塊間手性不對稱宏觀力的研究

胡永紅，靳海芹，毛彩霞

(1.湖北科技學(xué)院核技術(shù)與化學(xué)生物學(xué)院，湖北 咸寧 437100,2.湖北第二師范學(xué)院物理與電子信息學(xué)院，湖北 武漢 430205)

0 引言

1 手性宏觀勢

軸子在核子和電子間傳遞的相互作用有效勢為:

(1)

圖1-石英和吸引質(zhì)量銅塊的幾何構(gòu)形示意圖

(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)

根據(jù)如下的位置矢量變換：Prkj(r)P-1=-rkj,自旋的變換PσkP-1=σk和磁場的變換PBP-1=B.方程(3)對應(yīng)(2)式勢的不同手性，取相反的符號.

(5)

上式中的矩陣元乘積可以采用單電子近似簡化.利用等式:(σi·A)(σj·B)=A·B+iσi·(A×B)對電子自旋求和，矩陣元可以重寫為：

(6)

其中，|Ψk0〉和|Ψkn〉分別描述第i個原胞中第k個電子的初態(tài)和末態(tài).

2 矩陣元乘積的討論

(7)

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

(8)

3 結(jié)論分析及討論

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