Related papers: Generalized Ladder Operators for Shape-invariant P…
Quantum mechanical models and practical calculations often rely on some exactly solvable models like the Coulomb and the harmonic oscillator potentials. The $D$ dimensional generalized Coulomb potential contains these potentials as limiting…
In this paper, we classify the fundamental solutions for a class of Schrodinger operators.
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…
A method based on supersymmteric (SUSY) quantum mechanics has been developed by exploiting conditional Shape invariance property for obtaining exact ground state solution of generalized polynomial potential with Coulomb term. Specific cases…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
We prove the validity of regularizing properties of a double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in Schauder spaces by…
Let $M$ be a Riemannian manifold, $\tau: G \times M \to M$ an isometric action on $M$ of an $n$-torus $G$ and $V: M \to \mathbb R$ a bounded $G$-invariant smooth function. By $G$-invariance the Schr\"odinger operator, $P=-\hbar^2…
We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases…
We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition…
We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In…
We study one-dimensional Schr\"{o}dinger operators $\mathrm{S}(q)$ on the space $L^{2}(\mathbb{R})$ with potentials $q$ being complex-valued generalized functions from the negative space $H_{unif}^{-1}(\mathbb{R})$. Particularly the class…
Three sets of ladder operators in spheroconal coordinates and their respective actions on Lam\'e spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
Given a potential $V$ and the associated Schr\"odinger operator $-\Delta+V$, we consider the problem of providing sharp upper and lower bound on the energy of the operator. It is known that if for example $V$ or $V^{-1}$ enjoys suitable…
We count invertible Schr\"odinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fieldsfor trees, cycles and complete graphs.This is achieved for trees through the definition and use of local invariants…
We provide a summary of the continuity properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator…
Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\"odinger operator with a complex-valued potential.
We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…
A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. However, the complete hidden symmetry algebra and the…
This is mostly a survey paper, where we collect results concerning the spectral bounds of deterministic and random Schr\"odinger operators with complex potentials, both on \(\mathbb{R}^d\) and on compact manifolds. The survey part is…