  High-precision approximate analytic expressions for energies and wave
functions are found for arbitrary physical potentials. The Schr\"{o}dinger
equation is cast into nonlinear Riccati equation, which is solved analytically
in first iteration of the quasi-linearization method (QLM). The zeroth
iteration is based on general features of the exact solution near the
boundaries. The approach is illustrated on the Yukawa potential. The results
enable accurate analytical estimates of effects of parameter variations on
physical systems.
