Physical representations of Gamow states in a rigged Hilbert space

Resonant Gamow States (GS) are constructed in a rigged Hilbert space (RHS) (ξ, H, ξ′) starting from Diracʹs formula. It is shown that the expectation value of a self-adjoint operator acting on a GS is real. The validity of recently proposed approximations to calculate expectation values on resonant states is discussed.