相关论文: Scattering Wave Functions at Bound State Poles
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
A two-channel problem is considered within a method based on first order differential equations that are equivalent to the corresponding Schr\"odinger equation but are more convenient for dealing with resonant phenomena. Using these…
An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex…
We obtain L2-series solutions of the nonrelativistic three-dimensional wave equation for a large class of non-central potentials that includes, as special cases, the Aharonov-Bohm, Hartmann, and magnetic monopole potentials. It also…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…
We establish soliton-like asymptotics for finite energy solutions to the Schr\"odinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold, converges to a sum of traveling…
We consider the elastic scattering and bound states of charged quantum particles moving in the Aharonov-Bohm and an attractive $\rho^{-2}$ potential in a partial wave approach. Radial solutions of the stationary Schr\"{o}dinger equation are…
In these notes the Born series for the $s$-wave scattering $a_0$ is calculated for a class of central potentials $V(r)$ up to sixth order in a dimensionless coupling strength $g$. Examples of exponentially decaying potentials as well…
For a selfadjoint Schr\"odinger operator on the half line with a real-valued, integrable, and compactly-supported potential, it is investigated whether the boundary parameter at the origin and the potential can uniquely be determined by the…
The article discusses the correctness of the assumption about the similarity of molecular continuum electron functions with wave functions in electron-atom scattering. The elastic scattering of slow particles by pair of non-overlapping…
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…
We discuss formation of an S-wave bound-state in finite volume on the basis of L\"uscher's phase-shift formula.It is found that although a bound-state pole condition is fulfilled only in the infinite volume limit, its modification by the…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…