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云南师范大学学报:自然科学版

SO(3)群构造下角动量算符的矩阵元表示

王长荣

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

在不计及自旋的情况下,根据SO(3)群群元的生成条件和角动量算符(J)的三维空间转动情况,以较为简明的方式导出了地(J)2和(J)z所组成的以|j,m〉为基矢的共同表象中,角动量平方算符2及角动量算符(J)各分量的矩阵元表示.

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在样品池条件下,利用原子荧光光谱方法,测量了Rb(5D)He,Ar,H2碰撞中5D→7S的激发能量转移截面。获得的荧光包括由激发态产生的直接荧光部分和由于碰撞布居态而产生的敏化荧光部分。在不同的猝灭气体压强下,测量了相关的两部分荧光的相对荧光强度,得到了Rb(5D)与He,Ar和Hz碰撞的5D→7s转移截面分别为(1.2±0.3)×10^-17cm^2,(1.3±0.3)×10^-18cm^2和(8.3±2.1)×10^-17cm^2。同时确定了Rb(7S)与He,Ar和H2的碰撞猝灭速率系数。7s态与H2的碰撞猝灭速率系数1.7×10^-10cm^3·s^-1比Rb(7S)与He,Ar的大得多,它是反应与非反应速率系数之和,利用实验数据确定Rb(7S)与H。的反应截面为(1.O±0.4)×10^-16cm^2,Rb(5D)与H2反应截面为(7.1±2.9)×10^-17cm^2。Rb(7S)与H2的反应活动性大于Rb(5D)。
Composing ppp-adic qubits: from representations of SO(3)p_pp​ to entanglement and universal quantum logic gates
In the context of ppp-adic quantum mechanics, we investigate composite systems of ppp-adic qubits and ppp-adically controlled quantum logic gates. We build on the notion of a single ppp-adic qubit as a two-dimensional irreducible representation of the compact ppp-adic special orthogonal group SO(3)p_pp​. We show that the classification of these representations reduces to the finite case, as they all factorise through some finite quotient SO(3)p_pp​ mod pkp^kpk. Then, we tackle the problem of ppp-adic qubit composition and entanglement, fundamental for a ppp-adic formulation of quantum information processing. We classify the representations of SO(3)p_pp​ mod ppp, and analyse tensor products of two ppp-adic qubit representations lifted from SO(3)p_pp​ mod ppp. We solve the Clebsch-Gordan problem for such systems, revealing that the coupled bases decompose into singlet and doublet states. We further study entanglement arising from those stable subsystems. For p=3p=3p=3, we construct a set of gates from 444-dimensional irreducible representations of SO(3)p_pp​ mod ppp that we prove to be universal for quantum computation.