In a recent paper published in this Journal, Khordad and Sedehi (J Low Temp Phys 190(3):200, 2018 ) have studied the thermodynamic properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. In that meritorious research the energy of the system was obtained by solving the Schrödinger equation. The radial equation was mapped into a confluent hypergeometric differential equation and the differential equation associated to z coordinate was mapped into a biconfluent Heun differential equation. In this paper, it is pointed out a misleading treatment on the solution of the biconfluent Heun equation. It is shown that the energy $$E_{z}$$ E z can not be labeled with $$n_{z}$$ n z and this fact jeopardizes the results of this system. We calculate the partition function with the correct energy spectrum and recalculate the specific heat and entropy as a function of low and high temperatures.

中文翻译：

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双环状量子点在低温和高温下的热力学性质的备注

在本期刊最近发表的一篇论文中，Khordad 和 Sedehi (J Low Temp Phys 190(3):200, 2018 ) 研究了 GaAs 双环形量子点在外部磁场和电场下的热力学性质。在这项杰出的研究中，系统的能量是通过求解薛定谔方程获得的。径向方程被映射为合流超几何微分方程，与 z 坐标相关的微分方程被映射为双合流 Heun 微分方程。本文指出了对双汇合Heun方程解的误导处理。结果表明，能量$$E_{z}$$E z 不能用$$n_{z}$$$ nz 标记，这一事实危及该系统的结果。