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The positions of the $l=0$ $S$-matrix poles are calculated in generalized Woods-Saxon (GWS) potential and in cut-off generalized Woods-Saxon (CGWS) potential. The solutions of the radial equations are calculated numerically for the CGWS…
The motion of l=0 antibound poles of the S-matrix with varying potential strength is calculated in a cutoff Woods-Saxon (WS) potential and in the Salamon-Vertse (SV) potential, which goes to zero smoothly at a finite distance. The pole…
The trajectories of S-matrix poles are calculated in the finite-range phenomenological potential introduced recently by P. Salamon and T. Vertse (SV). The trajectories of the resonance poles in this SV potential are compared to the…
We formulate the Born approximation for finding resonance poles in the complex plane for potential scattering problems. Using the method, we study the distribution of resonance poles for several scattering potentials. In particular, we find…
We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-$\delta'$ contact interaction at the well edge. This contact potential is defined by appropriate…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are…
The classical square well potential is smoothed with a finite range smoothing function in order to get a new simple strictly finite range form for the phenomenological nuclear potential. The smoothed square well form becomes exactly zero…
In this study, we reveal the difference between Woods-Saxon (WS) and Generalized Symmetric Woods-Saxon (GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr\"odinger eq. for the two…
A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method…
Whether one starts form the analytic S-matrix definition or the requirement of gauge parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value s of energy squared. The complex number s…
Searching for infrastructure of the quantum mechanical system, we study trajectories of the s-wave poles of the S-matrix element with respect to a real phase $\alpha$ in the complex momentum plane for a complex extension of real potentials…
We discuss in general terms pole trajectories of resonances coupling to a continuum channel as some strength parameter is varied. It is demonstrated that, regardless the underlying dynamics, the trajectories of poles that couple to the…
We analyze the structure of the scattering matrix, $S(k)$, for the one dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of anti-bound poles, there exist an infinite number…
We consider the heavy quark-antiquark potential in the AdS / QCD correspondence, focusing in particular on a recently calculated AdS-like metric deformed by back-reaction effects. We find that tuning the long-distance behaviour of the…
The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for $l=0$ by setting the…
In a universe with a cosmological constant, the large-scale gravitational potential varies in time and this is, in principle, observable. Using an N-body simulation of a $\Lambda$CDM universe, we show that linear theory is not sufficiently…
We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of…
A Woods-Saxon equivalent to a double folding potential in the surface region is obtained for the heavy-ion scattering potential. The Woods-Saxon potential has fixed geometry and was applied as a bare potential in the analysis of…
Quarkonium resonances in the complex-mass scale are studied. Relativistic quark potential model is used to describe the quark-antiquark system. The complex-mass formula is obtained from two exact asymptotic solutions for the QCD motivated…