Related papers: Maslov index for power-law potentials
In this paper the Stewart-Lyth inverse problem is rewritten using the comoving scales as the basic parameter. It is shown that some information on the inflaton potential can be obtained from observations taking into account only the scalar…
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and the properties of the optimal…
Radial wave functions for power-law potentials are approximated with the help of power-law substitution and explicit summation of the leading constituent WKB series. Our approach reproduces the correct behavior of the wave functions at the…
We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be…
A relativistic Coulomb-like resummation factor in QCD is suggested, based on the solution of the quasipotential equation.
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
By using the integration by parts formula of a Markov operator, the closability of quadratic forms associated to the corresponding invariant probability measure is proved. The general result is applied to the study of semilinear SPDEs,…
In this paper we reconsider the formulation for the computation of the Casimir energy in spherically symmetric background potentials. Compared to the previous analysis, the technicalities are much easier to handle and final answers are…
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective…
Let $M=Q(i\sqrt{d})$ be any imaginary quadratic field with a positive square-free $d$. Consider the polynomial \[ f(x)=x^3-ax^2-(a+3)x-1, \] with a parameter $a\in Z$. Let $K=M(\alpha)$, where $\alpha$ is a root of $f$. This is an infinite…
We consider a general class of infinite dimensional reversible differential systems. Assuming a non resonance condition on the linear frequencies, we construct for such systems almost invariant pseudo norms that are closed to Sobolev-like…
A note that points out the possibility to have p<1 in Sobolev type of inequalities by a use of the momomial structure of polynomials or power series. The proof is simple: Triangle angle inequality p*>1, monomial estimate from p* to exponent…
We study the inverse Robin problem for the Schr\"odinger equation in a half-space. The potential is assumed to be compactly supported. We first solve the direct problem for dimensions two and three. We then show that the Robin-to-Robin map…
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and characterize the optimal functions. A…
We obtain eigenvalues and eigenfunctions of the Schr\"{o}dinger equation with a hyperbolic double-well potential. We consider exact polynomial solutions for some particular values of the potential-strength parameter and also numerical…
The multidimensional extension of the Aleskerov-Golubenko polarization index is developed. Several versions of the polarization index are proposed based on different distance functions. Basic properties of the index are examined.
The Schrodinger equation for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states energies. Additionally, the corresponding wave functions are expressed by the Jacobi polynomials. The…
We study the one-dimensional wave equation with an inverse power potential that equals $const.x^{-m}$ for large $|x|$ where $m$ is any positive integer greater than or equal to 3. We show that the solution decays pointwise like $t^{-m}$ for…
In this paper we study the index of reducibility of powers of a standard parameter ideal. An explicit formula is proved for the extremely case. We apply the main result to compute Hilbert polynomials of socle ideals of standard parameter…