= Double-well tunneling splitting
{title2=$E_{\pm}=E_{\rm well}\mp\hbar Ke^{-S_I/\hbar}$}
A symmetric two-well system has nearly localized left/right states coupled by a positive <quantum tunnelling> magnitude $\Delta=\hbar Ke^{-S_I/\hbar}$. Its effective <Hamiltonian> is $E_{\rm well}I-\Delta\sigma_x$, so the superposition with an <even> spatial <wavefunction> is lower, and the level splitting is $2\Delta$. The <dilute instanton gas> reproduces these two exponents through even/odd crossing sums.
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