Abstract In this article, approximate analytical bound state solutions of the Schrodinger equation in two-dimensional space for screened cosine Kratzer potential (SCKP) under the influence of the magnetic field and Aharanov-Bohm flux field have been investigated. We obtained energy eigenvalues and wave functions for SCKP with external fields (magnetic field and Aharanov-Bohm flux field) via parametric Nikiforov-Uvarov (pNU) method using the approximation method suggested by Greene-Aldrich for handling centrifugal barriers. We deduced energy eigenvalues for screened Kratzer potential (SKP) and Hellmann potential (HP) from the obtained energy spectrum of SCKP with an external field. We extended our results in D dimensions for Hellmann potential in the absence of external fields. Thermodynamical properties such as partition function Z ( ( B → ) , Φ A B , β ) , mean energy U ( B → , Φ A B , β ) , mean free energy F ( B → , Φ A B , β ) , entropy S ( B → , Φ A B , β ) , specific heat capacity C s ( B → , Φ A B , β ) , magnetization at finite temperature ( B → , Φ A B , β ) and magnetic susceptibility χ m ( B → , Φ A B , β ) at finite temperature is presented. The obtained numerical results for SKP and Hellmann potential are in a very good agreement with numerical results available in the literature with and without external fields respectively.

中文翻译：

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磁场和Aharanov-Bohm通量场影响下屏蔽余弦Kratzer势的束缚态解和热力学性质

摘要 本文研究了在磁场和Aharanov-Bohm 磁通场影响下筛选余弦Kratzer 电位(SCKP) 二维空间中薛定谔方程的近似解析束缚态解。我们通过参数化 Nikiforov-Uvarov (pNU) 方法使用 Greene-Aldrich 建议的处理离心障碍的近似方法获得了具有外部场（磁场和 Aharanov-Bohm 通量场）的 SCKP 的能量特征值和波函数。我们从获得的具有外场的 SCKP 的能谱中推导出筛选的 Kratzer 势 (SKP) 和 Hellmann 势 (HP) 的能量特征值。我们在没有外部场的情况下扩展了 Hellmann 势的 D 维结果。热力学性质，如分配函数 Z ( ( B → ) ，Φ AB , β ) , 平均能量 U ( B → , Φ AB , β ) , 平均自由能 F ( B → , Φ AB , β ) , 熵 S ( B → , Φ AB , β ) , 比热容 C s ( B → , Φ AB , β ) 、有限温度下的磁化强度 ( B → , Φ AB , β ) 和有限温度下的磁化率 χ m ( B → , Φ AB , β )。获得的 SKP 和 Hellmann 势的数值结果与文献中分别有和没有外场的数值结果非常吻合。