相关论文: Bargmann potentials and Marchenko transformations
A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully…
In this paper we consider a class of logarithmic Schr\"{o}dinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions by adapting some arguments of the Fountain theorem, and…
We study the nonlinear Schrodinger equations with a linear potential. A change of variables makes it possible to deduce results concerning finite time blow up and scattering theory from the case with no potential.
We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit…
A study is undertaken to investigate an analytical solution for the N-dimensional Schr\"{o}dinger equation with the Morse potential based on the Laplace transformation method. The results show that in the Pekeris approximation, the radial…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
In this paper, the Schrodinger equation for s-wave and arbitrary angular momenta with the Modified Mobuis Square potential is investigated respectively. The eigenfunctions as well as energy eigenvalues are obtained in an exact analytical…
The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schr{\"o}dinger and parabolic type…
Extending the point canonical transformation approach in a manner distinct from the previous ones, we propose a unified approach of generating potentials of all classes having non-constant masses.
We investigate the solutions for a time dependent potential by considering two scenarios for the fractional Schr\"odinger equation. The first scenario analyzes the influence of the time dependent potential in the absence of the kinetic…
We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…
In this paper, we give estimates of the solutions to Schr\"{o}dinger equation on modulation spaces with vector potential of sub-linear growth.
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
We present some physically interesting, in general non-stationary, one-dimensional solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed recently. The solutions include a coherent state, a phase-modified…
We obtain a representation of pairing energies in phase space, for the Lipkin-Meshkov-Glick and general boson Bardeen-Cooper-Schrieffer pairing models. This is done by means of a probability distribution of the quantum state in phase space.…
We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{\"o}dinger equation to the magnetic Schr{\"o}dinger equation. That is in presence of a magnetic potential. We establish…
The formalism developed in Refs.\cite{Guo:2023ecc,Guo:2024zal} that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the…
We analyze a recent pedagogical proposal for an alternative treatment of the angular part of the Schr\"odinger equation with a central potential. We show that the authors' arguments are unclear, unconvincing and misleading.
Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few- and many-body systems. We are extending for this purpose the quantum inversion approach for systems…
The electroweak phase transition in the Two-Higgs-Doublet Model is investigated. The Gibbs potential at finite temperature is computed with regard for the one-loop plus ring diagram contributions. The strong first-order phase transition…