  New solvable one-dimensional quantum mechanical scattering problems are
presented. They are obtained from known solvable potentials by multiple Darboux
transformations in terms of virtual and pseudo virtual wavefunctions. The same
method applied to confining potentials, e.g. P\"oschl-Teller and the radial
oscillator potentials, has generated the {\em multi-indexed Jacobi and Laguerre
polynomials}. Simple multi-indexed formulas are derived for the transmission
and reflection amplitudes of several solvable potentials.
