Abstract
We compare the asymptotic formulas for splitting higher and lower energy levels for the one-dimensional Schrödinger operator with the double-well potential. We establish that the splitting value for the lower energy level is proportional to that calculated for the higher levels with the factor \(\sqrt {e/\pi } \). An analogous result is found for the width of bands in the periodic case.
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Albeverio, S., Dobrokhotov, S.Y. & Semenov, E.S. Splitting Formulas for the Higher and Lower Energy Levels of the One-Dimensional Schrödinger Operator. Theoretical and Mathematical Physics 138, 98–106 (2004). https://doi.org/10.1023/B:TAMP.0000010637.91646.c2
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DOI: https://doi.org/10.1023/B:TAMP.0000010637.91646.c2