EVOLUTION OF COHERENT STATES OF A CHARGED PARTICLE IN A TIME DEPENDENT MAGNETIC FIELD

HUANG XIANG-YOU, TIAN XU, HU CHENG-LI

摘要 在Ｌａｎｄａｕ规范下计算出均匀磁场中带电粒子的圆心相干态。利用这些圆心相干态可方便地描述带电粒子的圆周运动。这些圆周运动与经典力学的结果比较表明，圆心相干态描述系综中的平均运动． Abstract Under Landau gauge center coherent states of charged particles in a uniform magnetic field are derived. It is convenient by use of these coherent states to describe the circular motion of charged particles in the field. The comparison between the circular motion and the result of classical mechanics shows that a center coherent state describes the averaged motion of an ensemble. 作者及机构信息 黄湘友1, 田旭3, 胡城立2 (1)北京大学物理系; (2)湖南大学机械系; (3)华中理工大学激光技术国家重点实验室 基金项目: 国家自然科学基金资助的课题. Authors and contacts HUANG XIANG-YOU1, TIAN XU3, HU CHENG-LI2 (1)北京大学物理系; (2)湖南大学机械系; (3)华中理工大学激光技术国家重点实验室 参考文献 施引文献

I.A. Malkin, Vladimir I. Man’ko, D. A. Trifonov

Ram K. Varma, A. M. Punithavelu

We report here experimental results which point to a rather unexpected, astonishing behavior of charged particle motion in a magnetic field in the presence of a retarding electric potential. An electron beam, when energy scanned with respect to its ‘parallel’ energy using a retarding potential, the response of the transmitted current as a function of the retarding potential is found to be oscillatory as against the monotonic response, expected according to the standard initial value paradigm of classical mechanics. The unexpected ‘peaks’ and ‘dips’ in the transmitted current plots are interpreted as “allowed” and “forbidden” energy states of the system. The peaks (or dips) are found to fit very well with a theoretical relationship which motivated the search for such a behavior; also “quantum numbers” for the peaks have been identified. A very astonishing aspect of the relationship is the dependence of the energies of the allowed states on the length of the box.

I.A. Malkin, Vladimir I. Man’ko, D. A. Trifonov

HUANG XIANG-YOU, Quanhui Liu, TIAN XU +2 more

Double wave quantum theory is applied to describe the motion of charged particle in a uniform magnetic field. This description of the motion of the particle is complete. One can tell the value of an arbitrary physical quantity at any time. The probability and the formula to calculate mean values in ordinary quantum mechanics comes from the average of double wave description over a certain ensemble. The rule of gauge transformation in quantum mechanics can be seen from the average over an ensemble.

V. V. Dodonov