Description:
<jats:p>Using the double phase-integral approximation technique developed earlier for the wave equation d2ψ/dz2+Q2(z) ψ=0, we derive analytical formulas for the reflection (R), transmission (T), and absorption (A) coefficients. They are valid to arbitrary order in the expansion parameter, for functions Q2(z) having either two cutoffs or one cutoff and one resonance. For two examples of this type the formulas for R, T, and A are checked against numerical results, using approximations up to fifth order.</jats:p>