WKB corrections to the energy splitting in double well potentials
  By using the WKB quantization we deduce an analytical formula for the energy splitting in a double--well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the double square well potential, the inverted harmonic oscillator and the quartic potential. 
Marko Robnik, Luca Salasnich and Marko Vranicar