We analyze the short-time behavior of the survival probability in the frame of the Friedrichs model for different formfactors. We have shown that this probability is not necessary analytic at the time origin. The time when the quantum Zeno effect could be observed is found to be much smaller than usually estimated. We have also studied the anti-Zeno era and have estimated its duration.

We propose a technique which is suitable for calculations of resonant energies of three-body systems. It is based on a smooth exterior complex scaling procedure and the three-dimensional finite-element method. Accuracy dependencies on an exterior radius and on a curvature of the rotated path are examined. S-wave resonances of helium are calculated with an accuracy better than 10 Ϫ5 a.u.

The eigenenergies and root mean square radii of the rovibrational levels (J = 0-3) of the weakly bound bosonic van der Waals neon trimer were calculated using a full angular momentum three-dimensional finite element method. The differing results of three previous studies for zero angular momentum are discussed, explained, and compared with the results presented here.

Abstract. -Based on the work of Nuttall and Cohen [Phys. Rev. 188 (1969) 1542] and Resigno et al. [Phys. Rev. A 55 (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schrödinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.Introduction. -Few-body systems held together by a mutual Coulomb interaction are of great interest in many areas of quantum physics. However, solving the Coulomb scattering problem is a very difficult task both from the theoretical as well as the computational points of view due to the long-range character of the Coulomb interaction. The asymptotic boundary conditions for the wave function at large separations between particles are already complicated for the few-body scattering problem with shortrange interactions [1]. They become even more complicated for the long-range case when the Coulomb potential is present in the interaction [2]. Therefore, a method which allows the problem to be solved without explicit use of the asymptotic form of the wave function is of great interest from both the theoretical and computational points of view.One of such methods was proposed by Nuttal and Cohen [3]. The approach is based on the complex scaling theory [4]. The idea can briefly be formulated as follows.The Schrödinger equation is recast into its inhomogeneous (driven) form by splitting the wave function into the sum Ψ = Ψ in + Ψ sc of the incident Ψ in and scattered Ψ sc waves as

We study the short-time and medium-time behavior of the survival probability in the frame of the N -level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may oscillate significantly during the so-called exponential era. This result explains qualitatively the experimental observations of the NaI decay.

The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complementary situations, firstly, when the interior part of the Coulomb potential is left in the Hamiltonian and, secondly, when the long-range tail is considered as the potential. The partial wave results are summed up to obtain the wavefunction in three dimensions. It is shown that in the domains where the wavefunction is expected to be proportional to the known solutions, the proportionality is given by an operator acting on the angular part of the wavefunction. The explicit representation for this operator is obtained in the basis of Legendre polynomials. We proposed a driven Schrödinger equation including an inhomogeneous term of the finite range with purely outgoing asymptotics for its solution in the case of the three-dimensional scattering problem with long-range potentials.

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