will introduce an additional linear time dependence in the decay law has been known for long time [@R15], only it was not clear what the vector was that evolved in this way. This vector $\mid z_d^-\rangle^{(1)}$ has now been defined. In addition the new result (\[ar22-2\]) shows that the different values of $k$ get mixed up by the time evolution.

Whereas there is no doubt that ordinary, $0$-order, Gamow vectors will be the suitable vectors to describe resonance states because of their properties II.1…II.5 above we have no idea what the physical meanining of the higher order Gamow vectors may be, if any. In contrast to the fact that ordinary Gamow states have been identified in abundance, e.g., through their Breit-Wigner profile in scattering experiments, or the exponential decay law [@R5], there is no convincing evidence for the existence of higher order poles in nature [@R6]. The k-th order Gamow states and their time evolution (\[ar22-2\]) are completely new and unusual. Their effect should also be so overwhelming that the meager evidence for higher order poles of the $S$-matrix which has been discussed in the past ($A_2$-splitting in particle physics, $^8\mbox{Be}$ in nuclear physics) would not be able to account 