Related papers: Quantum anharmonic oscillator and its statistical …
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to…
The determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy, namely the Wronskian of two solutions of the Schroedinger equation which are regular respectively at…
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the…
In this work we study a class of anharmonic oscillators within the framework of the Weyl-H\"ormander calculus. The anharmonic oscillators arise from several applications in mathematical physics as natural extensions of the harmonic…
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…
A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying effects produced by statistical operator or…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
We present in details a numerical approach for solving supersymmetric quantum mechanical systems with a gauge symmetry valid in all fermionic sectors. The method uses a recursive algorithm to calculate matrix elements of any gauge invariant…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
We have studied the underlying algebraic structure of the anharmonic oscillator by using the variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a…