ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS

DAI XIAN-XI; NI GUAN-JIONG

Chinese Physics C> 1978, Vol. 2> Issue(3) : 225-235

ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS

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Abstract：
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.

References

[1]

戴显熹,复旦学报,1977, 1, 100.[2] Y. Kazama, C. N. Yang, A. S. Goldhaber, Scattering of a Dirac particle with charge ze by a fixed magnetic monopole, SB-ITP 76/63.[3] 戴显熹、倪光炯,复旦学报,1977, 3, 1.[4] 戴显熹、沈纯理、昊子仪,“含磁荷奇异原子的光谱强度和选择规则”(兼论天文光谱观察中寻求磁荷的可能性), 1977年天文会议(黄山)论文集.[5] Y. Kazama, C. N. Yang, Existence of bound states for a charged spin 1/2 particle with an extra magnetic moment in the field of a fixed Mágnetic monopole, SB-Itp 76/65.

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DAI XIAN-XI and NI GUAN-JIONG. ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS[J]. Chinese Physics C, 1978, 2(3): 225-235.

DAI XIAN-XI and NI GUAN-JIONG. ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS[J]. Chinese Physics C, 1978, 2(3): 225-235. shu

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Received: 1977-09-16
Revised: 1900-01-01

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ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS

DAI XIAN-XI
NI GUAN-JIONG

Received Date: 1977-09-16
Accepted Date: 1900-01-01
Available Online: 1978-06-05

Abstract: 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.