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We show how the Laplace transform can be used to give a solution of the time-dependent Schr\"odinger equation for an arbitrary initial wave packet if the solution of the stationary equation is known. The solution is obtained without summing…

Quantum Physics · Physics 2016-08-01 Natascha Riahi

We study the final state problem for the nonlinear Schr\"{o}dinger equation with a critical long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic profile which is different from the free evolution, we…

Analysis of PDEs · Mathematics 2025-04-11 Masaki Kawamoto , Haruya Mizutani

We outline a general method of obtaining exact solutions of Schroedinger equations with a position dependent effective mass. Exact solutions of several potentials including shape invariant potentials have also been obtained.

Quantum Physics · Physics 2007-05-23 B. Roy , P. Roy

Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…

Mathematical Physics · Physics 2013-12-09 Valery Kapshai , Yury Grishechkin

It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…

Quantum Physics · Physics 2017-12-05 Hasan Hüseyin Erbil

In this paper, we use the variational method, especially the perturbation method, to find the perturbed high energy solutions of the quadratic coupled Schrodinger system with asymmetric asymptotic potential and their asymptotic behavior as…

Analysis of PDEs · Mathematics 2022-11-21 Mingyang Han , Kai Zhang

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

In this work, the analytical solution of the hyper-radial Schr\"{o}dinger equation for the spherical Woods-Saxon potential in D dimensions is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris…

Mathematical Physics · Physics 2011-11-22 V. H. Badalov , H. I. Ahmadov

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…

Analysis of PDEs · Mathematics 2015-11-17 Anton Savostianov

Reconstructing a radial (1D) quantum potential, V(r), from a few bound-state energies is a long-standing inverse problem because limited spectral data must constrain an entire potential. We present a Laplace-moment reconstruction pipeline…

Spectral Theory · Mathematics 2026-05-13 M. Gage Plott , F. Ayça Çetinkaya , Rick Mukherjee

In a recent paper Cari\~nena et al analyzed a non-polynomial one-dimensional quantum potential representing an oscillator which they argued was intermediate between the harmonic and isotonic oscillators. In particular they proved that it is…

Quantum Physics · Physics 2009-02-19 Jonathan M Fellows , Robert A Smith

The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be…

Computational Physics · Physics 2007-05-23 F. Buisseret , C. Semay

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…

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

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of…

Quantum Physics · Physics 2015-06-16 Sameer M. Ikhdair , Babatunde J. Falaye

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…

Quantum Physics · Physics 2009-11-10 Ramazan Koc , Hayriye Tutunculer

We show that the exact solution of the Schr\"odinger equation for two electrons confined to two distinct concentric rings or spheres can be found in closed form for particular sets of the ring or sphere radii. In the case of two concentric…

Chemical Physics · Physics 2015-06-12 Pierre-François Loos , Peter M. W. Gill

We obtain exact solitary wave solutions of a variant of the generalized derivative nonlinear Schrodinger\equation in 1+1 dimensions with arbitrary values of the nonlinearity parameter $\kappa$ in a Scarf-II potential. This variant of the…

Pattern Formation and Solitons · Physics 2018-11-14 Avinash Khare , Fred Cooper , John F. Dawson

This work presents exchange potentials for specific orbitals calculated by inverting Hartree-Fock wavefunctions. This was achieved by using a Depurated Inversion Method. The basic idea of the method relies upon the substitution of…

Atomic and Molecular Clusters · Physics 2016-10-21 A. M. P. Mendez , D. M. Mitnik , J. E. Miraglia

Approximate analytic solutions of the Dirac equation with Tietz-Hua (TH) potential are obtained for arbitrary spin-orbit quantum number using the Pekeris approximation scheme to deal with the spin-orbit coupling terms In the presence of…

Quantum Physics · Physics 2012-10-05 Sameer M. Ikhdair , Majid Hamzavi

In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum principle for the linearized equation and apply it to show that…

Analysis of PDEs · Mathematics 2021-03-16 Ru-Yu Lai , Ting Zhou