The accuracy of the WKB approximation when predicting the energy splitting of bound states in a double well potential is the main subject of this paper. The splitting of almost degenerate energy levels below the top of the barrier results from the tunneling and is thus supposed to be exponentially small. By using the standard WKB quantization we deduce an analytical formula for the energy split...

Asymptotics of the perturbation series for the ground state energy of the coupled anharmonic oscillators for the positive coupling constant is related to the lifetime of the quasistationary states for the negative coupling constant. The latter is determined by means of the multidimensional WKB approximation for tunneling along curved escape paths. General method for obtaining such approximation...

Established populations often exhibit oscillations in their sizes that, in the deterministic theory, correspond to a limit cycle in the space of population sizes. If a population is isolated, the intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a stochastic version of the Rosenzweig-MacArthur predator-pr...

In this work, we determined the analytical expressions of the form factor of a cubical particle in the WKB approximation. We adapted some variables (size parameter, refractive index, the scattering angle) and found the form factor in the approximation of Rayleigh-Gans-Debye (RGD), Anomalous Diffraction (AD), and determined the efficiency factor of the extinction. Finally, to illustrate our form...