Related papers: Accurate calculation of resonances in multiple-wel…
The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wave function for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete and it is given as a…
We investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalised complex eigenvalues of a non-selfadjoint deformation of the two-centers Schr\"odinger…
The correct numerical calculation of the resonance characteristics and, principally, the quality factor $Q$ of contemporary photonic and plasmonic resonant systems is of utmost importance, since $Q$ defines the bandwidth and affects…
A program is created to compute recursively the Moshinsky brackets. It is very fast and provides highly accurate results. In the case of the double-precision computations with a single-processor consumer notebook, the computing time per…
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with…
Quantum-mechanical WKB-method is elaborated for the known quantum oscillator problem in curved 3-spaces models Euclid, Riemann, and Lobachevsky E_{3}, H_{3}, S_{3} in the framework of the complex variable function theory. Generalized…
Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of relativistic wave equation for the coulombic and linear components of the potential are used to derive the resonance…
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…
We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
The eigenvalues of a new microbeam-rigid-body gyroscope are computed and studied to show the variation of frequencies versus the input spin rate. To this end, assuming the harmonic solution of the dynamic equation of motion the…
We give a new quantum circuit approximation of quantum multiplexors based on the idea of complexity theory oracles. As an added bonus, our multiplexor approximation immediately gives a quantum circuit approximation of diagonal unitary…
Quantum particle is considered confined in a toy-model potential possessing multiple minima. For the specific choice of the family of potentials (in the form of harmonic oscillator plus several logarithmic infinitely high but penetrable…
We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly…
In this paper we establish existence and multiplicity of solutions for an elliptic system which has strong resonance at first eigenvalue. To describe the resonance, we use an eigenvalue problem with indefinite weight. In all results we use…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…