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In some quantum mechanical problems involving singular states usually exists phase angle uncertainty. Recently in the investigation of the scattering of a Dirac particle with the charge Ze and a fixed magnetic monopole, Kazama, Yang and Goldharber [2] introduced some extra magnetic moments in order to eliminate the phase angle uncertainty. In this paper, instead of introducing any extra magnetic moment we use the adjusted framework of quantum mechanics suggested in [3], the criterion of orthogonality and the...

In some quantum mechanical problems involving singular states usually exists phase angle uncertainty. Recently in the investigation of the scattering of a Dirac particle with the charge Ze and a fixed magnetic monopole, Kazama, Yang and Goldharber [2] introduced some extra magnetic moments in order to eliminate the phase angle uncertainty. In this paper, instead of introducing any extra magnetic moment we use the adjusted framework of quantum mechanics suggested in [3], the criterion of orthogonality and the variation principle of energy (indefinite phase as a variation parameter) to determine the phase angle, the scattering cross section and the bound states uniquely. These principles for the determination of the solution have been tested for its correctness, because the result is consistent with the solution of reference [2]. By using these principles the problems of scattering and bound states of systems consisting of a charged magnetic monopole and a charged Dirac particle, as well as the monopole pair are exactly solved.

在量子力学的某些问题中,常常存在相角的不定性.最近在研究不动的电中性磁荷与荷电Dirac粒子的散射问题中,风间洋一、杨振宁和Goldhaber为了消除相角不定性,引入了附加磁矩.本文不引入附加磁矩,而利用文章中所建议的调整了的量子力学框架、正交判据和能量的变分原则(不定相角作为变分参数)唯一地确定了相角、散射截面和束缚态.由于结果与[2]的一致,使这些定解原则受到一次检验.利用这些定解原则,解决了荷电磁荷与荷电Dirac粒子及正负磁荷对偶的散射态和束缚态等问题.

In this paper four kinds of singular state problems in relativistic quantum me-chanics and its solutions are summarized. In the references [2,3,5,6,11], it hasbeen pointed out that in some quantum mechanial problems involving singular statesthere exists phase angle uncertainty. The principle eliminating this kind of nncer-tainty——the orthogonality-variation principle has been obtained in [11] The re-sults of scattering and bound state problems of a neutral monopole and a chargedDirac particle are consistent...

In this paper four kinds of singular state problems in relativistic quantum me-chanics and its solutions are summarized. In the references [2,3,5,6,11], it hasbeen pointed out that in some quantum mechanial problems involving singular statesthere exists phase angle uncertainty. The principle eliminating this kind of nncer-tainty——the orthogonality-variation principle has been obtained in [11] The re-sults of scattering and bound state problems of a neutral monopole and a chargedDirac particle are consistent with those obtained by C. N. Yang, Kazama, and Gold-haber. In [5], [11] and this paper the Case-type equations determining the boundstates of monopole pair and exotic atoms consisting of a charged monopole and anelectron are obtained. In this paper these energy levels are calculated numericallyBecause in these equations the number of singular points is infinite and the rune-tions oscillate rapidly, usual calculation methods are not suitable in these cases. Afteranalysing these equations and determining the positions of singular points and theranges of energy levels, these energy levels are calculated by computer. It is pointed out that the number of these energy levels is infinite and the posi-tions of positive and negative energy levels are asymmetric. The negative energylevels do not appear untilεis very near -1. The values of the positive energy levelsare spread in the range 0.9998(?)ε<1 They are near those of the hydrogen-like atomand similar to those of impurity in solid. This is a perturbation problem of singularstates to which the usual perturbation theory can not be applied. The energy levels of monopole pair are not similar to those of the hydrogen-likeatom. In the range 0<|ε|≤0.99 there are many energy levels with positive andnegative energy. It is also pointed out that for the hydrogen-like atoms, 119

本文综述了相对论量子力学中的四类奇性态问题及其解法。在文献[2,3,5,6,11]中,曾指出某些含奇性态的量子力学问题中,常存在相角不定性。[11]中曾获得消除这类不定性的原则——“正交-变分原则”。对于中性磁荷和荷电Dirac粒子的散射及束缚态的结果与杨振宁、风间洋一及Goldhaber的结果一致。在[5,11]和本文中得到了确定磁荷及含荷电磁荷和电子的奇异原子的束缚态的方程。本文对这些能级作了数值计算。由于在这些方程中奇点数目是无穷多的,并且函数振荡极快,通常的计算方法不适用。经过对方程作分析及确定奇点的位置和能级的区域后,将这些能级用计算机算出。指出这些能级数目是无穷的,正负能级的位置是不对称的,负能级仅在ε非常接近-1时才出现。正能级展布在区域0.9998(?)ε<1中。它们接近于类氢原子的能级并与固体中的杂质能级相似。这是一个通常微扰理论不能适用的奇性态微扰问题。磁荷偶的能级与类氢原子不相像。在区域0<|ε|≤0.99中,已具有许多正负能级。本文还指出,对于119

本文综述了相对论量子力学中的四类奇性态问题及其解法。在文献[2,3,5,6,11]中,曾指出某些含奇性态的量子力学问题中,常存在相角不定性。[11]中曾获得消除这类不定性的原则——“正交-变分原则”。对于中性磁荷和荷电Dirac粒子的散射及束缚态的结果与杨振宁、风间洋一及Goldhaber的结果一致。在[5,11]和本文中得到了确定磁荷及含荷电磁荷和电子的奇异原子的束缚态的方程。本文对这些能级作了数值计算。由于在这些方程中奇点数目是无穷多的,并且函数振荡极快,通常的计算方法不适用。经过对方程作分析及确定奇点的位置和能级的区域后,将这些能级用计算机算出。指出这些能级数目是无穷的,正负能级的位置是不对称的,负能级仅在ε非常接近-1时才出现。正能级展布在区域0.9998(?)ε<1中。它们接近于类氢原子的能级并与固体中的杂质能级相似。这是一个通常微扰理论不能适用的奇性态微扰问题。磁荷偶的能级与类氢原子不相像。在区域0<|ε|≤0.99中,已具有许多正负能级。本文还指出,对于119

There are different thoughts about the tectonic evolutions of palaeotethyan stage in South China and Qinling belt,which are mainly due to the lack of reliable chronology evidences of the strata in those belts.The method of research orogenic strata is proposed in this paper.The major developments on the deep water facies palaeontology and stratigraphy in South China and Qinling belt made in last years are reviewed.The authors point out that many continental blocks different in size,distributed around Yangtze...

There are different thoughts about the tectonic evolutions of palaeotethyan stage in South China and Qinling belt,which are mainly due to the lack of reliable chronology evidences of the strata in those belts.The method of research orogenic strata is proposed in this paper.The major developments on the deep water facies palaeontology and stratigraphy in South China and Qinling belt made in last years are reviewed.The authors point out that many continental blocks different in size,distributed around Yangtze plate,were surrounded by deep water sea basins and limited ocean basins.Yangtze plate and the group of those blacks were a part of the global palaeotethyan archipelagoes ocean.

对于华南及秦岭造山带的大地构造演化存在不同的认识,其关键问题是地层时代的归属不同。笔者提出造山带地层的研究方法,对华南及秦岭地区近年来深水相古生物学及地层学研究进展进行了综述。指出海西—印支期扬子板块周缘存在许多大小不等的陆块,它们被不同海域性质的深水盆地包围,扬子板块及这些陆块群为全球古特提斯多岛洋的一个组成部分

 
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