  I investigate whether it is possible to generate bound-states from resonances
or virtual states through first-order perturbation theory. Using contact-type
potentials as those appeared in pionless effective field theory, I show that it
is possible to obtain negative-energy states by sandwiching a next-to-leading
order (NLO) interaction with the leading-order (LO) wavefunctions, under the
presence of LO resonances or virtual states. However, at least under the
framework of time-independent Schr\"odinger equation and Hermitian Hamiltonian,
there is an inability to create bound-states with structure similar to those
formed by the non-perturbative treatments.
