Localization or tunneling in asymmetric double-well potentials

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• 作者：Dae-Yup Song ^{dsong@sunchon.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quantum tunneling ; Localization ; Double-well potential
• 刊名：Annals of Physics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：362
• 期：Complete
• 页码：609-620
• 全文大小：414 K

文摘

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the wells with negligible magnitude in the other. Using Dekker’s method (Dekker, 1987), the present analysis generalizes earlier results for weakly biased double-well potentials to systems with arbitrary asymmetry.