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We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…

Atomic Physics · Physics 2009-11-13 A. D. Alhaidari

A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…

Quantum Physics · Physics 2007-05-23 Bodo Hamprecht

We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…

Mesoscale and Nanoscale Physics · Physics 2023-11-27 R. M. Lima , H. R. Christiansen

The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulth\'{e}n potential with any spin-orbit quantum number $\kappa$. Solutions are obtained by using an appropriate coordinate transformation,…

Quantum Physics · Physics 2015-05-19 Altug Arda , Ramazan Sever , Cevdet Tezcan

In this paper, we consider the existence, orbital stability/instability and regularity of bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions for the mass…

Analysis of PDEs · Mathematics 2025-10-14 Tianxiang Gou , Xiaoan Shen

The consistency of the concept of quantum (quasi)particles possessing effective mass which is both position- and excitation-dependent is analyzed via simplified models. It is shown that the system may be stable even when the effective mass…

Quantum Physics · Physics 2014-02-14 Miloslav Znojil , Géza Lévai

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…

Computational Physics · Physics 2015-05-14 William A. Karr , Christopher R. Jamell , Yogesh N. Joglekar

In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrodinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the…

An upgraded concept of solvability of Schr\"{o}dinger-type equations is proposed. In a broader methodical context of non-perturbative quantum theory the innovation involves potentials which are piece-wise analytic yielding differential…

Quantum Physics · Physics 2016-05-10 Miloslav Znojil

We obtain an exact solution of the time-dependent Schroedinger equation for a two-electron system confined to a plane by an isotropic parabolic potential whose curvature is periodically modulated in time. From this solution we compute the…

Condensed Matter · Physics 2009-10-31 Irene D'Amico , Giovanni Vignale

An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…

Mathematical Physics · Physics 2008-04-24 Christiane Quesne

With the aid of a modified similarity transformation we obtained exact energy eigenvalues of the generalized Dirac-Coulomb equation. This equation consists of the time component of the Lorentz 4-vector potential V_v(r)=-A_1/r, and a Lorentz…

Mathematical Physics · Physics 2007-05-23 Omar Mustafa , Thabit Barakat

We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of…

Analysis of PDEs · Mathematics 2024-11-28 Irina Nenciu , Xiaoan Shen , Christof Sparber

The object of this paper is to investigate, classically and quantum mechanically, the relation existing between the position-dependent effective mass and damping-antidamping dynamics. The quantization of the equations of motion is carried…

Quantum Physics · Physics 2015-03-19 Yamen Hamdouni

We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…

High Energy Physics - Phenomenology · Physics 2020-01-03 Viktor Andreev

Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…

Quantum Physics · Physics 2009-11-11 I. O. Vakarchuk

In this research, the radial Schrodinger equation for a newly proposed screened Kratzer-Hellmann potential model was studied via the conventional Nikiforov-Uvarov method. The approximate bound state solution of the Schrodinger equation was…

Quantum Physics · Physics 2021-07-28 Gabriel T. Osobonye , Uduakobong S. Okorie , Precious O. Amadi , Akpan N. Ikot

A closed-form solution to the energy-based stochastic Schrodinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist…

Quantum Physics · Physics 2007-05-23 Dorje C. Brody , Irene C. Constantinou , James D. C. Dear , Lane P. Hughston

We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3+1)-dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are…

Mathematical Physics · Physics 2009-06-09 Sameer M. Ikhdair

It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant…

Mathematical Physics · Physics 2015-05-13 T. K. Jana , P. Roy