二维反谐振子在恒定垂直外磁场下的逗留时间

粒子逗留时间的计算是量子力学基本问题之一. 本文对处于垂直外磁场下的二维反谐振势模型运用费曼路径积分方法, 得到了初始时刻位于原点的高斯波包随时间的演化方程, 然后计算了带电粒子的逗留时间. 根据计算结果讨论了初始高斯波包在不同宽度情况下, 磁场对逗留时间的影响. 结果显示, 逗留时间刚开始随着磁场强度的增加单调增加, 但当磁场强度足够大, 使得拉莫尔频率?c超过谐振子频率?0时, 逗留时间将变成无穷大, 这与三维情况下的逗留时间仍然持续增加的结果有很大不同.

The sojourn time of the inverted 2D harmonic oscillators under a constant perpendicular magnetic field

The calculation of sojourn time is a fundamental problem in quantum mechanics. In this paper, we study the magnetic effects on the sojourn time of the two-dimensional (2D) charged inverted harmonic oscillator under a constant perpendicular magnetic field. We obtain the time evolution of a Gaussian wave-packet initially centered at the origin by employing the Feynman path integral approach, followed by acquiring the integral expression for the sojourn time. Consequently, the magnetic effect on the sojourn time for the Gaussian wave-packets with different values of the initial width are discussed. It is shown that the sojourn time works as a function of the strength of the magnetic field increase. However, when the strength of the magnetic field is so large that the Larmor frequency passes over the inverted harmonic oscillator frequency, the sojourn time becomes infinity. This finding is quite different from the 3D case in which it remains an increasing function.