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Related papers: An extended scenario for the Schrodinger equation

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The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The…

Quantum Physics · Physics 2019-12-06 Cevdet Tezcan , Ramazan Sever

The potentials $V (v)$ in the nonrelativistic (relativistic) nucleon-nucleon (NN) Schroedingerequation are related by a quadratic equation. That equation is numerically solved, thus providing phase equivalent v- potentials related for…

Nuclear Theory · Physics 2008-11-26 H. Kamada , W. Gloeckle

The exact solutions of the Schrodinger equation with the hyperbolic Scarf potential reported in the literature so far rely upon Jacobi polynomials with imaginary arguments and parameters. We here show that upon a suitable factorization…

Quantum Physics · Physics 2008-11-26 D. E. Alvarez-Castillo , M. Kirchbach

The solution of the Schrodinger equation with a linear potential is considered. We use algebraic methods to obtain the explicit form of the solution for the explicitly time dependent Hamiltonian and discuss the general conditions which…

Mathematical Physics · Physics 2010-10-11 G. Dattoli , K. Zhukovsky

An algebraic non-perturbative approach is proposed for the analytical treatment of Schr\"{o}dinger equations with a potential that can be expressed in terms of an exactly solvable piece with an additional potential. Avoiding disadvantages…

Quantum Physics · Physics 2009-11-10 B. Gonul , N. Celik , E. Olgar

A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=\alpha_o q^2 +…

Quantum Physics · Physics 2009-11-06 Omar Mustafa , Maen Odeh

The Schroedinger equation with one and two dimensional potentials are solved in the frame work of the sl(2) Lie algebra. Eigenfunctions of the Schroedinger equation for various asymmetric double-well potentials have been determined and the…

Quantum Physics · Physics 2007-05-23 Ramazan Koc , Derya Haydargil

For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…

Exactly Solvable and Integrable Systems · Physics 2024-12-03 Andrei D. Polyanin , Nikolay A. Kudryashov

We analyze the application of the "tridiagonal representation approach" (TRA) to the Schr\"{o}dinger equation for some simple, exactly-solvable, quantum-mechanical models. In the case of the Kratzer-Fues potential the mathematical reasoning…

Quantum Physics · Physics 2024-12-17 Francisco M. Fernández

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…

Quantum Physics · Physics 2007-05-23 C. Quesne

This paper follows on from a previous one in which it was shown that it is possible, within a de Broglie-Bohm style ontology for quantum mechanics, to incorporate action and reaction between the particle and its guiding field while…

Quantum Physics · Physics 2019-11-19 Roderick Sutherland

An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…

Mathematical Physics · Physics 2009-11-07 A. D. Alhaidari

The Self-Adjoint Extension in the Schrodinger equation for potentials behaved as an attractive inverse square at the origin is critically reviewed. Original results are also presented. It is shown that the additional solutions must be…

Mathematical Physics · Physics 2009-09-03 T. Nadareishvili , A. Khelashvili

It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential.…

Quantum Physics · Physics 2013-12-17 Peter Holland

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in…

Exactly Solvable and Integrable Systems · Physics 2007-09-12 Tuncay Aktosun , Francesco Demontis , Cornelis van der Mee

We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…

Quantum Physics · Physics 2010-03-30 Wei Khim Ng , Rajesh R. Parwani

We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of…

Mathematical Physics · Physics 2016-09-15 Thierry Combot

We compare two recent approaches of quasi-exactly solvable Schr\" odinger equations, the first one being related to finite-dimensional representations of $sl(2,R)$ while the second one is based on supersymmetric developments. Our results…

Quantum Physics · Physics 2009-11-07 Y. Brihaye , N. Debergh , J. Ndimubandi

The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et…

Nuclear Theory · Physics 2015-06-12 Sergio Deflorian , Nir Barnea , Winfried Leidemann , Giuseppina Orlandini

The Self-Adjoint Extension in the Schrodinger equation for potentials behaved as an attractive inverse square at the origin is critically reviewed. Original results are also presented. It is shown that the additional non-regular solutions…

High Energy Physics - Theory · Physics 2012-10-16 Teimuraz Nadareishvili , Anzor Khelashvili