Related papers: On the quantum-mechanical singular harmonic oscill…
We show that a perturbed Coulomb problem discussed recently is conditionally solvable. We obtain the exact eigenvalues and eigenfunctions and compare the former with eigenvalues calculated by means of a numerical method. We discuss the…
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…
Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…
Employing the phase-space representation of second order ordinary differential equations we developed a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for quantum model…
Perturbation expansions up to third order for the generalized spiked harmonic oscillator Hamiltonians H = -d^2/dx^2+ x^2 + A/x^2 + lambda/x^alpha, A >= 0, 2gamma > alpha, gamma=1+(1/2)sqrt(1+4A), and small values of the coupling lambda > 0,…
We build a new estimate relative with Hermite functions based upon oscillatory integrals and Langer's turning point theory. From it we show that the equation $$ i \partial_t u =-\partial_x^2 u+x^2 u+\epsilon \langle x\rangle^{\mu} W(\nu…
We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple…
The quantum version of a non-linear oscillator, previouly analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form $m={(1+\lambda x^2)}^{-1}$ and with a…
The non-Hermitian PT-symmetric quantum-mechanical Hamiltonian $H=p^2+x^2(ix)^\epsilon$ has real, positive, and discrete eigenvalues for all $\epsilon\geq 0$. These eigenvalues are analytic continuations of the harmonic-oscillator…
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
A short introduction of a relation between a Green's function and a quantum wave impedance function as well as its application to a determination of eigenenergies and eigenfunctions of a quatum-mechanical system is provided. Three different…
We use the Hellman-Feynman (HF) and Hypervirial (HV) theorems, to calculate the perturbative coefficients of the eigenenergies formal series, in the case of the Coulomb potential with a radial linear term and the radial quartic anharmonic…
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various…
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum.…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…
We discuss spectral properties of the family of quartic oscillators $\mathfrak h_{\mathcal M}(\alpha) =-\frac{d^2}{dt^2} +\Big(\frac{1}{2} t^{2} -\alpha\Big)^2$ on the real line, where $\alpha\in \mathbb{R}$ is a parameter. This operator…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…