Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling

Abstract

We discuss the leading asymptotics of eigenvalue splittings of - 2 + X2V in the limit as X -- o, and where V is a non-negative potential with several zeros. For example, if EO(X), E1(X) are the two lowest eigenvalues in -a situation where V has precisely two zeros, a and b, related by a symmetry, then limx . - (X)-lIn[E1(X) - EO(X)] is given as the distance from a to b in a certain Riemann metric.