Related papers: Supersymmetric generalized power functions
Spectral parameter power series (SPPS) representations for solutions of Sturm-Liouville equations proved to be an efficient practical tool for solving corresponding spectral and scattering problems. They are based on a computation of…
A spectral parameter power series (SPPS) representation for regular solutions of singular Bessel type Sturm-Liouville equations with complex coefficients is obtained as well as an SPPS representation for the (entire) characteristic function…
We perform the characterization program for the supersymmetric configurations and solutions of the $\mathcal{N}=1$, $d=5$ Supergravity Theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general…
We show that electronic wave functions Psi of atoms and molecules have a representation Psi=F*phi, where F is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution Psi itself, and phi has…
In this paper we propose the idea of expanding the space of variations in standard variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi: \psi = \psi[\chi]$, rather…
We study in this paper very badly approximable matrix functions on the unit circle $\T$, i.e., matrix functions $\Phi$ such that the zero function is a superoptimal approximation of $\Phi$. The purpose of this paper is to obtain a…
For real bounded functions \Phi and \Psi of compact support, we prove the norm resolvent convergence, as \epsilon and \nu tend to 0, of a family of one-dimensional Schroedinger operators on the line of the form S_{\epsilon, \nu}=…
In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both…
In this paper, we determine all irreducible spherical functions \Phi of any K -type associated to the pair (G,K)=(\SO(4),\SO(3)). This is accomplished by associating to \Phi a vector valued function H=H(u) of a real variable u, which is…
We review the closed-forms of the partial Fourier sums associated with $HP_k(n)$ and create an asymptotic expression for $HP(n)$ as a way to obtain formulae for the full Fourier series (if $b$ is such that $|b|<1$, we get a surprising…
We evaluate certain multidimensional integrals in terms of the Lerch transcendent function $\Phi$, generalizing Guillera-Sondow's formulas. As an application, we get new representations of classical constants like Euler's constant $\gamma$…
In the 1995 paper entitled "Noncommutative symmetric functions," Gelfand, et. al. defined two noncommutative symmetric function analogues for the power sum basis of the symmetric functions, along with analogues for the elementary and the…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $\chi$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of…
We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher…
In this paper we consider a nonlinear generalization of the isotonic oscillator in the same spirit as one considers the generalization of the harmonic oscillator with a truly nonlinear restoring force. The corresponding potential being…
Introduced eighty years ago, the Fermi pseudopotential has been a powerful concept in multiple fields of physics. It replaces the detailed shape of a potential by a delta-function operator multiplied by a parameter giving the strength of…
We consider nonclassical entropy solutions to scalar conservation laws with concave-convex flux functions, whose set of left- and right-hand admissible states across undercompressive shocks is selected by a kinetic function \phi. We…
For any positive integer $k$ and nonnegative integer $m$, we consider the symmetric function $G\left( k,m\right)$ defined as the sum of all monomials of degree $m$ that involve only exponents smaller than $k$. We call $G\left( k,m\right)$ a…
Recent results using inverse scattering techniques interpret every solution $\phi (x,y)$ of the sine-Gordon equation as a non-linear superposition of solutions along the axes $x=0$ and $y=0$. Here we provide a geometric method of…