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Acta Physica Sinica

CALCULATION ON CENTER COHERENT STATES OF CHARGED PARTICLES IN A UNIFORM MAGNETIC FIELD UNDER LANDAU GAUGE

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

Published Jan 1, 1994• 0 citations
Publisher

Abstract

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

DOI
10.7498/aps.43.1913

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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.

Acta Physica Sinica•Jan 1, 1993•1 citation
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
Abstract In this paper we show how the classical result of a charged particle moving in a circle in the xy plane, when a uniform magnetic field is directed along the z -axis, can be derived from the Landau quantum theory using the coherent states of the two-dimensional isotropic harmonic oscillator in the xy plane. The coherent states in this case are the simultaneous eigen vectors of the annihilation operators a + and a − . We prove that the time-dependent coordinate space wave packets representing the time-dependent coherent states move in a circle with the cyclotron frequency ω c = ∣ q ∣ B m and with a radius given by the classical expression, but given in terms of the quantum mechanical expectation values. The expectation value of the energy of the particle and of the square of the radius of its circular are proportional to the square of the magnitude of the eigen value of a + in the coherent state, where as the x and y coordinates of the centre of the circle are proportional to the real and the imaginary parts of the eigen value of a − . The phase of the circular motion is the same as the phase of the complex eigen value of a + . So for a given energy of the particle or for a given radius of the circular orbit, there are an infinite number of circles which differ from each other by the x and y coordinates of the centre as well as the phase of the circular motion. The infinite degeneracy of the Landau levels is due to the invariance of the energy eigen values under spatial translations in the xy plane and rotations about the z -axis. We also show that as the magnitude of the eigen value of a + becomes much larger than one, the relative uncertainty or fluctuation in the energy and in the radius of the circular orbit becomes negligibly small as we expect for a classical state.
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.