Modified semiclassical quantization conditions for double minimum potentials: Applications to anharmonic oscillators

WKB-type connection formulas, established by Miller and Good and based on the quadratic mapping of a section of a potential containing a local minimum, are used to obtain ‘‘modified-well’’ quantization conditions for general double minimum potentials. Significant improvements in the usual WKB eigenvalues may be achieved by combining these with the corresponding ‘‘modified-barrier’’ rules. This is shown to be true in the context of the anharmonic oscillator potentials V(x)=-${\mathrm{kx}}^2$+λ$x^4$ (k,λ>0) for a wide range of λ. The characteristic features of the different modified formalisms are also discussed.