GAMOW STATES AS CONTINUOUS LINEAR FUNCTIONALS OVER ANALYTICAL TEST FUNCTIONS

The space of analytical test functions xi, rapidly decreasing on the r eal axis (i.e., Schwartz test functions of the type S on the real axis ), is used to construct the rigged Hilbert space (RHS) (xi, H, xi'). G amow states (GS) can be defined in RHS starting from Dirac's formula, It is shown that the expectation value of a selfadjoint operator actin g on a GS is real. We have computed exactly the probability of finding a system in a GS and found that it is finite. The validity of recentl y proposed approximations to calculate the expectation value of self-a djoint operators in a GS is discussed. (C) 1996 American Institute of Physics.