The reading of this paper (which ``teaches by example'') only makes
sense if the reader knows what the authors mean by Quantum Mechanics
in which it is necessary to distinguish between ``states'' (defined
during preparation) and ``observables'' (determined by the
detector). Fortunately, a compact form of such an information is now
available, e.g., in the recent paper ``Time Asymmetric Quantum
Mechanics'' by A. R. Bohm, M. Gadella and P. Kielanowski, SIGMA 7
(2011), 086 (arXiv:1109.0598). Once you get familiar with this
theory and accept the underlying semigroup interpretation of quantum
evolution), it is a true pleasure to see all that illustrated by the
present, exactly solvable leaking-well example. The theory will give
you a few answers to obvious mathematical questions (e.g., why
should we start the calculations from the Green's functions) as well
as a basic explanation of its physical innovativeness (showing,
e.g., why should we represent a quantum system using rigged Hilbert
space (1)).
MR2810782 Domínguez, Aizar Enciso; Kielanowski, Piotr Time evolution
of the unstable quantum oscillator. Internat. J. Theoret. Phys. 50
(2011), no. 7, 2252--2258. 81Qxx