非对易相空间Dirac oscillator的研究(英文)

On the Dirac oscillator in the noncommutative phase space

在极坐标系中研究了非对易相空间中的Dirac oscillator问题.研究显示:系统的波函数可以表示为合流超几何函数,而非对易相空间Dirac oscillator的量子行为类似于朗道问题.最后,对μ=0和对易极限两种特殊情况进行了简单讨论.

In this letter the Dirac oscillator is studied in the noncommutative phase space which contains both the spatial noncommutativity and momentum noncommutativity. The analytical wave functions and corresponding energy levels are obtained in polar coordinates. It is shown that the analytical wave functions of the Dirac oscillator can be expressed in terms of confluent hypergeometric function in the noncommutative phase space and the Dirac oscillator problem in the noncommutative phase space has a similar behavior to the Landau problem. Finally, two special cases for η = 0 and for commutative limit are briefly discussed.