We calculate resonances, antibound states and two new light induced states
of the dressed one-dimensional attractive delta -function potential, as fun
ction of alpha (0) - the free electron quiver motion amplitude in a monochr
omatic electromagnetic field, in the range 0 < alpha (0) < 150 a.u. We desc
ribe also our method, adequate to the numerical solution of the Schrodinger
equation for this particular potential. (C) 2001 Elsevier Science B.V. All
rights reserved.