Semi-analytic version of shooting method and the bound states in   non-analytic potential $V(x)= -g^2\exp (-|x|)$
  People construct quantum bound states either non-numerically (in not too many exceptional cases) or, in general, numerically (mainly using majorization or discretization techniques). We point out that there exists a class of interactions "in between". Being, in conventional terminology, neither exactly solvable nor purely numerical. The idea is illustrated by the elementary exponential-well toy-model potential $V(x)= -g^2\exp (-|x|)$. 
Miloslav Znojil
quant-ph