Related papers: Anharmonic oscillator and the optimized basis expa…
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
We take an additional step towards the optimization of the novel finite-range pseudopotential at constrained Hartree-Fock-Bogolyubov level and implement an optimization procedure within an axial code using harmonic oscillator basis. We…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number…
In the present article, we describe a method of introducing the harmonic potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.
We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that…
We analyse the one dimensional quartic oscillator using the effective operator methodology of Lee and Suzuki. We reproduce known results for low lying energy eigenvalues.
The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential $\lambda x^4$ is discussed for real and imaginary time. The first order results in the imaginary time formalism provide…
We continue our previous application of supersymmetric quantum mechanical methods to eigenvalue problems in the context of some deformed canonical commutation relations leading to nonzero minimal uncertainties in position and/or momentum.…
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D.…
We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…
The aim of this paper is twofold. First of all, we study the behaviour of the lowest eigenvalues of the quantum anharmonic oscillator under influence of an external field. We try to understand this behaviour using perturbation theory and…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and…
We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…