相关论文: The Relativistic Linear Singular Oscillator

Several properties of bound states in potential $ V(x)= g^2\exp (|x|)$ are studied. Firstly, with the emphasis on the reliability of our arbitrary-precision construction, wave functions are considered in the two alternative (viz.,…

Non-relativistic potential models are considered of the pure power V(r) = sgn(q) r^q and logarithmic V(r) = ln(r) types. Envelope representations and kinetic potentials are employed to show that these potentials are actually in a single…

A review on the Lorentz invariant treatment of neutrino spin and flavour oscillations in moving and polarized matter is presented. Within this approach it becomes possible to consider neutrino oscillations in arbitrary electromagnetic…

We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…

The focusing critical wave equation in three dimensions exhibits a special class of static solutions which are linearly unstable. These solutions decay like an inverse first power. We construct small codimension one stable manifolds in the…

A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several model systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Its order-by-order…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…

A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…

We analyze the supersymmetry and the shape invariance of the potentials of the (1+1) relativistic oscillators we have recently proposed.

A nonrelativistic decomposition for the quark energy by the ratio of the dispersion of quark momentum squared and the effective quark mass is investigated in the framework of the relativistic oscillator constituent quark model as bound…

In this work, we are interested in to study removability of a singular set in the boundary for some classes of quasilinear elliptic equations. We will approach this question in two different ways: through an asymptotic behavior at the…

We extend the exactly solvable Hamiltonian describing $f$ quantum oscillators considered recently by J. Dorignac et al. by means of a new interaction which we choose as quasi exactly solvable. The properties of the spectrum of this new…

We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special…

We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial…

In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation…

The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…

We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…

We present various exact solutions of a discrete complex Ginzburg-Landau (CGL) equation on a plane lattice, which describe target patterns and spiral patterns and derive their stability criteria. We also obtain similar solutions to a system…

We investigate the stabilizability of linear discrete-time switched systems with singular matrices, focusing on the spectral radius in this context. A new lower bound of the stabilizability radius is proposed, which is applicable to any…