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In this paper, we study a system of focusing fourth-order Schr\"odinger equations in the energy-critical setting with radial initial data and general power-type nonlinearities. The main idea is to generalize the analysis of such systems: we…

Analysis of PDEs · Mathematics 2025-09-05 Maicon Hespanha , Renzo Scarpelli

In this paper, we study the Schr\"odinger equation with a new quasi-exactly solvable double-well potential. Exact expressions for the energies, the corresponding wave functions and the allowed values of the potential parameters are obtained…

Mathematical Physics · Physics 2017-02-22 Marzieh Baradaran , Hossein Panahi

We cast the quantum chemistry problem of computing bound states as that of solving a set of auxiliary eigenvalue problems for a family of parameterized compact integral operators. The compactness of operators assures that their spectrum is…

Quantum Physics · Physics 2021-07-07 Gregory Beylkin , Joel Anderson , Robert J. Harrison

We consider the inhomogeneous Mixed-boundary value problem for the cubic nonlinear Schr\"{o}dinger equations on the half line. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions…

Analysis of PDEs · Mathematics 2019-10-31 Liliana Esquivel , Elena Kaikina , Nakao Hayashi

We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…

Quantum Physics · Physics 2022-03-14 A. D. Alhaidari , I. A. Assi , A. Mebirouk

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…

Quantum Physics · Physics 2008-12-23 F. Maiz , M. Nasr

Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…

Quantum Physics · Physics 2015-06-18 Huseyin Akcay , Ramazan Sever

We apply a simple transformation method to construct a set of new exactly solvable potentials (ESP) which gives rise to bound state solution of $D$-dimensional Schr\"odinger equation. The important property of such exactly solvable quantum…

Mathematical Physics · Physics 2014-02-07 Nabaratna Bhagawati

In this study, the Schrodinger equation for flat potentials through the pseudo-perspective method is investigated.

Computational Physics · Physics 2019-10-08 Vahid Mirzaei Mahmoud Abadi , Javad Mohammadi

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method.…

Quantum Physics · Physics 2009-11-13 Sameer M. Ikhdair , Ramazan Sever

We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire…

Quantum Physics · Physics 2008-11-26 Y. Meurice

We prove some existence (and sometimes also uniqueness) of weak solutions to some stationary equations associated to the complex Schr\''{o}dinger operator under the presence of a singular nonlinear term. Among other new facts, with respect…

Analysis of PDEs · Mathematics 2024-02-20 Pascal Bégout , Jesús Ildefonso Díaz

The general solutions of Schrodinger equation for non central potential are obtained by using Nikiforov Uvarov method. The Schrodinger equation with general non central potential is separated into radial and angular parts and energy…

Quantum Physics · Physics 2009-11-10 F. Yasuk , C. Berkdemir , A. Berkdemir

A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy…

Quantum Physics · Physics 2012-06-11 D. A. Kulikov , V. M. Shapoval

An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ\i es for various eigenstates and the corresponding wave functions are…

Quantum Physics · Physics 2007-05-23 Sameer M. Ikhdair , Ramazan Sever

We solve the Schr\"odinger equation with a position-dependent mass (PDM) charged particle interacted via the superposition of the Morse and Coulomb potentials and exposed to external magnetic and Aharonov-Bohm (AB) flux fields. The…

Quantum Physics · Physics 2017-05-10 Mahdi Eshghi , Hussein Mehraban , Sameer M. Ikhdair

By using the Pekeris approximation, the Schrodinger equation is approximately solved for the nuclear deformed Woods-Saxon potential within the framework of the asymptotic iteration method. The energy levels are worked out and the…

Nuclear Theory · Physics 2013-01-04 Babatunde J. Falaye , Majid Hamzavi , Sameer M. Ikhdair

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical…

Quantum Physics · Physics 2020-12-23 C. M. Ekpo , E. B. Ettah

We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…

Computational Physics · Physics 2021-06-16 M Gulliksson , M Ogren

The auxiliary field method, defined through introducing an auxiliary (also called as the Hubbard-Stratonovich or the Mean-) field and utilizing a loop-expansion, gives an excellent result for a wide range of a coupling constant. The…

High Energy Physics - Theory · Physics 2009-10-31 Taro Kashiwa