Related papers: Classical and Quantum Complexity of the Sturm-Liou…
We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via \Gamma-convergence theory, we study the asymptotic distribution of the minimizers as the…
Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite…
A Sturm-Liouville problem ($\lambda wy=(ry')'+qy$) is singular if its domain is unbounded or if $r$ or $w$ vanish at the boundary. Then it is difficult to tell whether profound results from regular Sturm-Liouville theory apply. Existing…
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite…
We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\left[ y^{\prime }+sy\right] )^{\prime }+sp\left[ y^{\prime…
This paper deals with the discrete system being the finite-difference approximation of the Sturm-Liouville problem with frozen argument. The inverse problem theory is developed for this discrete system. We describe the two principal cases:…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
Given a finite set of eigenvalues of a regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, the potential q(x) of which is unknown. We show the possibility to compute more eigenvalues without any additional…
In this paper, we shall derive a spectral matrix method for the approximation of the eigenvalues of (weakly) regular and singular Sturm-Liouville problems in normal form with an unbounded potential at the left endpoint. The method is…
In this paper, inequalities among eigenvalues of different self-adjoint discrete Sturm-Liouville problems are established. For a fixed discrete Sturm-Liouville equation, inequalities among eigenvalues for different boundary conditions are…
In this study, we consider a boundary value problem generated by the Sturm-Liouville problem with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and characteristic function…
In this paper, we consider the wave equation for the fractional Sturm-Liouville operator with lower order terms and singular coefficients and data. We prove that the problem has a very weak solution. Furthermore, we prove the uniqueness in…
We use the theory of entire functions of finite order to prove a universal spectral dependence of the blowup/decay rate of solutions of the Sturm-Liouville eigenvalue equation for problems with Schatten $p$-class resolvents. The general…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order 2S, acting on functions…
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…
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…
We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Pr\"ufer…
I study some possibilities of analytically solving a particular Sturm-Liouville problem with step-wise (piece-constant) coefficients with help of an iterative procedure mentioned in my previous paper (Green's function sum rules). I…
We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum…