Description:
<jats:p>The wave equation is solved with the phase-integral approximation in the asymptotic regions, and integrated numerically elsewhere. In this application the phase-integral approximation is relatively simple in higher orders, and its accuracy can be precisely controlled with the derived error estimates. For the bound states the analytical formulas defining the termination error in the wave function are derived. For the wave propagation an efficient formalism is given for calculating the reflection, transmission, and absorption coefficients.</jats:p>