Related papers: Upper and lower limits for the number of S-wave bo…
In a recent paper new upper and lower limits were given, in the context of the Schr\"{o}dinger or Klein-Gordon equations, for the number $N_{0}$ of S-wave bound states possessed by a monotonically nondecreasing central potential vanishing…
The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with the specifically…
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…
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…
We identify a class of potentials for which the semiclassical estimate $N^{\text{(semi)}}=\frac{1}{\pi}\int_0^\infty dr\sqrt{-V(r)\theta[-V(r)]}$ of the number $N$ of (S-wave) bound states provides a (rigorous) lower limit: $N\ge…
We establish bounds on the energy of a system of N identical bosons bound by attractive pair potentials and obeying the semirelativistic Salpeter equation. The lower bound is provided by a `reduction', with the aid of Jacobi relative…
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…
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 supersymmetric technique for the bound-state solutions of the s-wave Klein--Gordon equation with equal scalar and vector standard Eckart type potential is proposed. Its exact solutions are obtained. Possible generalization of our approach…
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…
Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of…
We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yields several sequences of upper and lower limits on the…
We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the…
We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the $N\bar{N}$ in $S$-wave (the quarks in the…
In the context of non-relativistic quantum mechanics, we obtain several upper and lower limits on the mean square radius applicable to systems composed by two-body bound by a central potential. A lower limit on the mean square radius is…
We derive an appropriate Landau-Ginzburg-Wilson effective action to describe the nearest neighbour attractive Hubbard model. This allows us to discuss both the small V (BCS) limit and the large V (Bose-Einstein) limit within the same…
We obtain the analytical solutions to the Schr\"odinger equation for the attractive inverse-square potential in an induced electric dipole moment system under the influence of the harmonic oscillator. We show that bound states can exist…
The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the…
We consider Schr\"odinger operators with smooth periodic potentials in Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on the density of states for large values of the spectral parameter.
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…