n维相对论粒子的量子态密度及其应用

The derivation and application of the density of quantum states for relativistic particle in n dimensions

利用半经典近似的方法,推导出了n维相对论自由粒子量子态密度以及黑体辐射中两类粒子的辐射公式的统一表达式,并且给出了低维情况下的表达式,所得结果与三维空间的预期结果一致.这对于深化低维体系的教学与研究具有重要的意义.

By the means of the semi-classical approximation, the density of quantum states for relativistic particles in n-dimensional space is derived and thus the lower dimensional results are obtained, and then apply it in the research of the black body radiation of n- dimensional space, the universal expressions of two kinds of particles in black body radiation is inferred, our main formulas which is yielded in the lower dimensions are consistent with our expected results for the three-dimensional space, which plays an important role for deepening the teaching and research in the lower dimensions.