二维Duffin-Kemmer-Petiau振子在外磁场作用下的热性质
Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length
摘要：
广义不确定原理提出了普朗克尺度下最短距离和/或最大动量的存在，以供考虑。本文研究了二维Duffin-Kemmer-Petiau（DKP）振子在外磁场中的最小长度（ML）解.首先，我们得到了普通量子力学中的本征解。然后，我们研究的DKP振荡器中存在的ML自旋零和自旋一部门。我们确定的能量本征值方程在这两种情况下，相应的本征函数在非相对论性的限制。我们表明，在普通的量子力学极限，ML修正消失，能量本征值方程变得与习惯的量子力学的相同。最后，利用欧拉-麦克劳林求和公式，得到了高温标度下DKP振子的热力学函数。
英文摘要：
Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin-Kemmer-Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler-Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.
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