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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.

Quantum Physics · Physics 2008-11-06 Nagalakshmi A Rao , B. A. Kagali

We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…

Quantum Physics · Physics 2007-05-23 Ramazan Koc , Hayriye Tutunculer , Eser Olgar

In this note we consider boundary value problems in electromagnetism. We prove well-posedness results for the time-harmonic Maxwell equations in the setting of Riemannian manifolds. We also consider the eigenvalue problem the homogeneous…

Analysis of PDEs · Mathematics 2019-07-02 Yernat M. Assylbekov

In this paper, we propose a new finite element approach, which is different than the classic Babuska-Osborn theory, to approximate Dirichlet eigenvalues. The Dirichlet eigenvalue problem is formulated as the eigenvalue problem of a…

Numerical Analysis · Mathematics 2020-01-16 Wenqiang Xiao , Bo Gong , Jiguang Sun , Zhimin Zhang

We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…

Quantum Physics · Physics 2017-12-07 M. I. Samar , V. M. Tkachuk

A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable $x$ and ${\d\over \d x}$ (the minimal canonical representation). The eigenstates of the Hamiltonian operator are found (at lower…

Mathematical Physics · Physics 2009-10-31 J. Guerrero , V. Aldaya

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…

Mathematical Physics · Physics 2015-06-05 F. Cannata , M. V. Ioffe , D. N. Nishnianidze

In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…

Quantum Physics · Physics 2019-10-02 Satoshi Ohya , Pinaki Roy

We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol…

Differential Geometry · Mathematics 2015-04-13 Andreas Malmendier

We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…

Quantum Physics · Physics 2015-06-26 P. Tempesta , E. Alfinito , R. A. Leo , G. Soliani

We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also…

Quantum Physics · Physics 2021-12-21 Domenico Giordano , Pierluigi Amodio

We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential $V(r)=(a^2\omega^2/4)sinh(r/a)^2$ where $a$ is the curvature radius and $r$ is the geodesic distance from a fixed center. Thus the potential is…

Mathematical Physics · Physics 2009-11-13 P. Stovicek , M. Tusek

We discuss some applications of the Morse-Novikov theory to some problems in modern physics, where appears a non-exact closed 1-form $\omega$ (a multi-valued functional). We focus mainly our attention to the cohomology of the de Rham…

Algebraic Topology · Mathematics 2007-05-23 Dmitri V. Millionschikov

We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of…

Quantum Physics · Physics 2018-01-17 Paolo Amore , Francisco M. Fernández

We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide…

Analysis of PDEs · Mathematics 2025-02-18 Pier Domenico Lamberti , Dirk Pauly , Michele Zaccaron

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…

High Energy Physics - Phenomenology · Physics 2009-10-28 Wolfgang Lucha , Franz F. SCHÖberl

A necessary and sufficient condition for a parameter transformation that leaves invariant the energy of a one dimensional autonomous system is obtained. Using a parameter transformation the Hamilton-Jacobi equation is solved by a…

Mathematical Physics · Physics 2007-05-23 G. Gonzalez

Approximate bound state solutions of the Dirac equation with -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary L-state. The energy eigenvalue equation and corresponding two-component wave…

Nuclear Theory · Physics 2013-08-02 Sameer M. Ikhdair , Majid Hamzavi

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…

High Energy Physics - Theory · Physics 2013-07-04 Sanjib Dey , Andreas Fring

We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator $V(x)=\alpha/(2x^2)+x^2/2$ by means of the simple and straightforward Frobenius (power-series) method. From the behaviour of the eigenfunctions at origin we…

Quantum Physics · Physics 2023-05-15 Francisco M. Fernández