标题： 对称双势阱势下薛定谔方程的精确解与WKB方法的比较：基态分裂的准确性 显示英文标题

标题： Exact solution of Schrödinger equation with symmetric double-well potential versus WKB: accuracy for ground state splitting

摘要： 一维对称三角双势阱（DWP）薛定谔方程通过角椭球函数精确求解。 对丙二醛中氢键基态分裂的严格解析计算结果与几种近似半经典（WKB）方法进行比较。 这使我们能够比较文献中提出的各种WKB公式的准确性：1. 普通WKB，即来自Landau和Lifshitz教科书的公式；2. Garg公式；3. 瞬子方法。 所得结果为丙二醛红外光谱实验数据的精确定量描述提供了一种新的理论工具。 显示英文摘要

摘要： The one-dimensional Schr\"odinger equation with symmetric trigonometric double-well potential (DWP) is exactly solved via angular oblate spheroidal function. The results of stringent analytic calculation for the ground state splitting of hydrogen bond in malonaldehyde are compared with several variants of approximate semiclassical (WKB) ones. This enables us to compare the accuracy of various WKB formulas suggested in the literature: 1. ordinary WKB, i.e., the formula from the Landau and Lifshitz textbook; 2. Garg's formula; 3. instanton approach. The results obtained provide a new theoretical tool for the precise quantitative description of experimental data on IR spectroscopy of malonaldehyde.