[en] A new method has been introduced for proving the asymptotic completeness in the case of potential scattering. This method was founded on geometrical concepts. A link is established between this method and the spectral transformation method

[en] A method of forming approximate representations for propagators with external field dependence is suggested and discussed in the context of potential scattering. An integro-differential equation in D+1 variables, where D represents the dimensionality of Euclidian space-time, is replaced by a Volterra equation in one variable. Approximate solutions to the latter provide a generalization of the Bloch-Nordsieck representation, containing the effects of all powers of hard-potential interactions, each modified by a characteristic soft-potential dependence

[en] The present paper is devoted to the scattering theory of a class of continuum Schrödinger operators with deterministic sparse potentials. We first establish the limiting absorption principle for both modified free resolvents and modified perturbed resolvents. This actually is a weak form of the classical limiting absorption principle. We then prove the existence and completeness of local wave operators, which, in particular, imply the existence of wave operators. Under additional assumptions on the sparse potential, we prove the completeness of wave operators. In the context of continuum Schrödinger operators with sparse potentials, this paper gives the first proof of the completeness of wave operators

[en] Let V element-of L_c^∞ (Rⁿ) be a real-valued potential, n ≥ 3 odd. The scattering matrix, Sv(A), corresponding to V extends to be a meromorphic function in C. Our normalization is that P, the physical half plane, is the open lower half plane, C^-. Thus, S_v(λ) only has a finite number of poles in P and they correspond to the bound states of the Hamiltonian Δ + V (Δ is the positive Laplacian). In Zworski has shown that the number of scattering poles n(r) in a disc of radius r is bounded by C(r + 1)ⁿ, and in he has given similar lower bounds for n(r) for certain radial potentials. The question of the existence of pure imaginary scattering poles was investigated by Lax and Phillips for both obstacle and potential scattering. In the case of obstacle scattering they showed that the number N(s) of pure imaginary scattering poles of absolute value less than s satisfies C₁ s²< N(s) for n = 3 for some constant C₁ > 0, and there is an analogous upper bound if the obstacle is star-shaped. They also proved that much of the machinery can be translated into the setting of potential scattering by non-negative potentials. This reduces the problem of obtaining lower bounds for N(s) to finding the corresponding bounds when V is tile characteristic function of a ball. In this paper we make the simple observation that their proof can be modified to accommodate non-positive potentials, and we prove that if V or -V is bounded below by a positive multiple of the characteristic function of a ball, then for some C, C' > 0

[en] We consider the semi-classical approximation of time-delay operators in potential scattering theory. We show that in non-trapping energy interval, Narnhofer's time-delay operator admits a semi-classical expansion in terms of pseudo-differential operators of class T₁¹. The classical limit for Eisenbud-Wigner time-delay operator is also given

[en] In this note we want to remedy the situation by providing a simple and systematic generalization of the eikonal equation as a general means to study high-energy scattering. (Author)

[en] Time-dependent schroedinger theory of potential scattering is numerically investigated in one-dimensional space. We have studied simple quantum mechanical systems by general algorithm on partial differential equation. Quantum scattering considered in this paper includes step, rectangular barrier, square-well, gaussian barrier and tanh-type barrier potentials. Results can be displayed on personal computor graphically. (Author)

[en] The Schroedinger operator in L²(Rsup(n)) with potential V=divergence of W is considered. W is a real Rsup(n) valued function such that (1) the local singularities of W² are controlled in a suitable sense by a kinetic energy (2) W tends to zero at infinity faster than r^-1. The Hamiltonian is defined by a method of quadratic forms and the usual results of scattering theory are derived; the negative spectrum is discrete and finite, the absolutely continuous spectrum is [0, infinite), the continuous singular spectrum is empty, the wave operators exist and are asymptotically complete

No abstract available

[en] An energy-independent optical potential is derived by projection operator techniques. Its properties are investigated in a simple model. (author)