相关论文: Asymptotic Inverse Problem for Almost-Periodically…
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…
We consider the perturbed harmonic oscillator $T_D\psi=-\psi''+x^2\psi+q(x)\psi$, $\psi(0)=0$, in $L^2(\R_+)$, where $q\in\bH_+=\{q', xq\in L^2(\R_+)\}$ is a real-valued potential. We prove that the mapping $q\mapsto{\rm spectral data}={\rm…
This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal…
The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and…
We discuss propagation of space-time singularities for the quantum harmonic oscillator with time-dependent metric and potential perturbations. Reformulating the quasi-homogeneous wave front set according to Lascar (1977) in a semiclassical…
We study the direct and inverse spectral problems for semiclassical operators of the form $S = S_0 +\h^2V$, where $S_0 = \frac 12 \Bigl(-\h^2\Delta_{\bbR^n} + |x|^2\Bigr)$ is the harmonic oscillator and $V:\bbR^n\to\bbR$ is a tempered…
We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bounded, whereas the spectra of position and momentum are a denumerable non-degenerate set of points in [-1,1] that depends on the…
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 study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter $\lambda $. The ground state can be obtained exactly and its energy…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…
The improvement of resummation algorithms for divergent perturbative expansions in quantum field theory by asymptotic information about perturbative coefficients is investigated. Various asymptotically optimized resummation prescriptions…
The O(N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions. The problem is directly related to that of a quantum double well anharmonic oscillator in an…
The article studies the Dirichlet and Dirichlet-Neumann problems for the Sturm-Liouville equation perturbed by an integral operator with a convolution kernel. Sharp asymptotic formulas for the eigenvalues of these problems are found. The…
A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown…