n维简谐势阱中粒子的态密度

The Density of States of Particles in a Harmonic Potential in Any Dimensional Space

应用半经典近似法计算任意维数非相对论性理想体系处于简谐外势中的量子态密度，得出解析的表达式，并进行讨论．揭示了简谐外势对系统性质的影响．特别是对于二维系统，使之从准长程序转变为长程序，对于一维系统。

By Using the semi classical approximation, the density of quantum states of the nonrelativistic ideal system in a harmonic potential is calculated, and the analytical results are derived for any dimensional systems. The effects of harmonic potential on the properties of such systems are expounded. It is shown that the effect of harmonic potential on the low dimensional system is quite evident, which makes the two dimensional system from quasi long range order to long range order and the one dimensional system from disorder to quasi long range order.