Gamow–Siegert functions and Darboux-deformed short range potentials

Darboux-deformations of short range one-dimensional potentials are constructed by means of Gamow–Siegert functions (resonance states). Results include both Hermitian and non-Hermitian short range potentials which are exactly solvable. As illustration, the method is applied to square wells and barriers for which the transmission coefficient is a superposition of Fock–Breit–Wigner distributions. Resonance levels are calculated in the long lifetime limit by means of analytical and numerical approaches. The new complex potentials behave as an optical device which both refracts and absorbs light waves.