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The one-dimensional Schr\"odinger equation with symmetric trigonometricdouble-well potential (DWP) is exactly solved via angular oblate spheroidalfunction. The results of stringent analytic calculation for the ground statesplitting of hydrogen bond in malonaldehyde are compared with several variantsof approximate semiclassical (WKB) ones. This enables us to compare theaccuracy 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 theprecise quantitative description of experimental data on IR spectroscopy ofmalonaldehyde.

Exact solution of Schr\"odinger equation with symmetric double-well potential versus WKB: accuracy for ground state splitting