We studied a class of exponential potential model \(V(x)=-a\,e^{-b\,x}\) (\(a>0, b>0\)) and found that its solutions are given by the Bessel functions, but the energy spectra \(E=-b^2(n+1/2)^2/8\) which are derived from the quantization condition do not correspond to any discrete bound states. The energy levels which are calculated by the boundary condition \(J_{\nu }(2\sqrt{2a}/b)=0\) at the origin are in good agreement with the numerical results. We illustrate the wave functions through varying the potential parameters a, b and notice that they are pull back to the origin when the potential parameter a or b increases.

我们研究了一类指数势模型\（V（x）=-a \，e ^ {-b \，x} \）（\（a> 0，b> 0 \））并发现其解已给出通过贝塞尔函数，但是从量化条件导出的能谱\（E = -b ^ 2（n + 1/2）^ 2/8 \）不对应于任何离散的束缚态。由边界条件\（J _ {\ nu}（2 \ sqrt {2a} / b）= 0 \）计算出的能级与数值结果非常吻合。我们通过改变电势参数a，b来说明波动函数， 并注意到当电势参数a或b增加时它们会拉回到原点。