  Abraham-Moses transformations, besides Darboux transformations, are
well-known procedures to generate extensions of solvable potentials in
one-dimensional quantum mechanics. Here we present the explicit forms of
infinitely many seed solutions for adding eigenstates at arbitrary real energy
through the Abraham-Moses transformations for typical solvable potentials, e.g.
the radial oscillator, the Darboux-P\"oschl-Teller and some others. These seed
solutions are simple generalisations of the virtual state wavefunctions, which
are obtained from the eigenfunctions by discrete symmetries of the potentials.
The virtual state wavefunctions have been an essential ingredient for
constructing multi-indexed Laguerre and Jacobi polynomials through multiple
Darboux-Crum transformations. In contrast to the Darboux transformations, the
virtual state wavefunctions generate non-polynomial extensions of solvable
potentials through the Abraham-Moses transformations.
