Related papers: Solve spheroidal wave functions by SUSY method
Supersymmetric quantum gauge theories are important mathematical tools in high energy physics. As an example, supersymmetric matrix models can be used as a holographic description of quantum black holes. The wave function of such…
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…
Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the $BC_n$ root system), we arrive -- via partial confluent limits in the sense of Oshima and Shimeno -- at solutions of the…
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical…
An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in…
Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric $g_{ik}=diag(1,-a^2)$. Several classes of particular solutions of these relations are…
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum…
Quantum Mechanics SUper-SYmmetry (QM-SUSY) provides a general framework for studies using phenomenological potentials for nucleons (or clusters) interacting with a core. The SUSY potentials result from the transformation of the mean field…
We study a SU(2)_L x U(1)_Y gauge theory in the Randall-Sundrum background, including electroweak symmetry breaking due to a brane-localized Higgs sector. We work in the decomposed four dimensional theory and treat the symmetry breaking…
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the…
A hyperbolic singularity in the wave-function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here we apply the transcorrelated method, whereby the wave-function singularity is explicitly described…
As demonstrated by Slepian et. al. in a sequence of classical papers, prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. Recently, PSWFs have been…
The spectrum of Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) in D=4 dimensions for SU(2) gauge group is computed for a maximal number of bosonic quanta $B\le60$ in the two-fermion sector with the angular momentum $j=0$. We analyse…
In this work, we first give various explicit and local estimates of the eigenfunctions of a perturbed Jacobi differential operator. These eigenfunctions generalize the famous classical prolate spheroidal wave functions (PSWFs), founded in…
We introduce a model of Poisson random waves in $\mathbb{S}^{2}$ and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity.…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.