具有非中心势的薛定谔方程：一些统计性质
Schrödinger Equation with a Non-Central Potential: Some Statistical Quantities
摘要：
本文研究了薛定谔方程的自由能、平均能、熵和比热等统计量对温度的依赖关系，特别是在非中心势的情况下.基本点是找到配分函数，该配分函数是通过基于Euler-Maclaurin公式的方法获得的。首先，我们给出了分析结果，并给出了一维和三维情况下的热函数图，以找出角动量的影响。我们还研究了非中心电位的角度依赖部分的影响。我们简要地讨论了系统的相变的结果。我们也给出了三维谐振子的结果。
英文摘要：
In this paper, we search the dependence of some statistical quantities such as the free energy, the mean energy, the entropy, and the specific heat for the Schrödinger equation on the temperature, particularly the case of a non-central potential. The basic point is to find the partition function which is obtained by a method based on the Euler-Maclaurin formula. At first, we present the analytical results by supporting with some plots for the thermal functions for one- and three-dimensional cases to find out the effect of the angular momentum. We also search then the effect of the angle-dependent part of the non-central potential. We discuss the results briefly for a phase transition for the system. We also present our results for three-dimesional harmonic oscillator.
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