A novel strategy to applying the analytical solution of the Schrödinger equation via angular prolate spheroidal (APS) function was developed. It provides a simple and accurate approach to calculating the energy levels, splitting and tunneling frequency in symmetrical double well potentials. The strategy consists of modeling the potential energy surface (PES) with an appropriate intrinsic reaction coordinate (IRC) curve, and its fitting to the solvable symmetric trigonometric potential. The parameter L is solved via the variation method. The accuracy was tested against using the same steps with the WKB method and the instanton-soliton approach to NH₃, ND₃ and methyl substituted amines. For NH₃, the tunneling frequencies were $2.56,3.67$ and $1.12\times {10}^{10}$ s⁻¹, using the APS function, WKB and instanton approaches respectively, while the experimental is $2.38\times {10}^{10}$ s⁻¹. The results show that it produced the most accurate results with a straightforward calculation, and in regions where the semi-classical fails.

提出了一种通过角扁球体（APS）函数应用薛定ding方程的解析解的新策略。它提供了一种简单而准确的方法来计算对称双阱势能中的能级，分裂和隧穿频率。该策略包括用适当的本征反应坐标（IRC）曲线对势能面（PES）进行建模，并将其拟合为可解决的对称三角势。参数L通过变化方法求解。使用WKB方法和瞬时孤子方法对NH ₃，ND ₃和甲基取代的胺使用相同的步骤测试了准确性。对于NH ₃，隧穿频率为$2.56，3.67$ 和 $1.12\times {10}^{10}$ s ^-1，分别使用APS函数，WKB和Instanton方法，而实验是$2.38\times {10}^{10}$ s ^-1。结果表明，它通过简单的计算以及在半经典失败的区域中产生了最准确的结果。