This work analytically solved the radial Schrödinger equation with an exponential, generalised, anharmonic Cornell potential using the series expansion method. It also obtained the bound state energy spectra. Through suitable adjustments to the potential parameters, the well-known potential models, such as the pseudoharmonic and Kratzer potentials, were deduced. With the potential parameters also adjusted, the energy spectra for the pseudoharmonic and Kratzer potentials were obtained as special cases. The numerical values of the energy spectra for CO, NO, CH and N₂ diatomic molecules were computed for different quantum numbers, n and l, respectively. In addition, with the application of the spectra, an expression for the mass spectra of heavy quarkonium systems (charmonium and bottomonium) was obtained. The results agree with the experimental and theoretical studies in previous works.

中文翻译：

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夸克-夸克相互作用势的径向薛定inger方程的束缚态解

这项工作使用级数展开法以指数形式，广义的非调和康奈尔势解析地求解了径向薛定ding方程。它还获得了束缚态能谱。通过对电势参数进行适当的调整，推导了众所周知的电势模型，例如拟谐波和Kratzer电势。在调整势能参数的情况下，获得了特谐谐波和Kratzer势能的能谱。计算了不同量子数n和l下CO，NO，CH和N ₂双原子分子的能谱数值， 分别。另外，通过使用光谱，获得了重的夸克铵体系（铵和bottom）的质谱表达式。研究结果与以往的实验和理论研究相吻合。