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For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…

Chemical Physics · Physics 2022-05-16 Jerry L. Whitten

The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…

Numerical Analysis · Mathematics 2018-08-31 Douglas Arnold , Guy David , Marcel Filoche , David Jerison , Svitlana Mayboroda

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In…

Quantum Physics · Physics 2015-05-13 Sameer M. Ikhdair , Ramazan Sever

New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the…

High Energy Physics - Theory · Physics 2017-05-03 M. G. Garcia , A. S. de Castro , P. Alberto , L. B. Castro

By applying an ansatz to the eigenfunction, an exact closed form solution of the Schr\"{o}dinger equation in 2D is obtained with the potentials, $V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and $V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$,…

Quantum Physics · Physics 2007-05-23 Shi-Hai Dong

We study the relativistic version of Schr\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states.…

High Energy Physics - Theory · Physics 2015-08-05 M. H. Al-Hashimi , A. M. Shalaby

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…

Quantum Physics · Physics 2018-03-13 F. D. Mazzitelli , M. D. Mazzitelli , P. I. Soubelet

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…

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

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…

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

We study the solution of the relativistic Schr\"odinger equation for a point particle in 1-d under $\delta$-function potential by using cutoff regularization. We show that the problem is renormalizable, and the results are exactly the same…

High Energy Physics - Theory · Physics 2014-06-24 M. H. Al-Hashimi , Abouzeid M. Shalaby

For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…

Chemical Physics · Physics 2022-05-16 Fariba Nazari , Jerry L. Whitten

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

Based on the Caputo fractional derivative the classical, non relativistic Hamiltonian is quantized leading to a fractional Schroedinger type wave equation. The free particle solutions are localized in space. Solutions for the infinite well…

Mathematical Physics · Physics 2007-05-23 Richard Herrmann

In this paper, the approximate analitical solutions of the hyper-radial Schr\"{o}dinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy…

Nuclear Theory · Physics 2026-05-01 V. H. Badalov , B. Baris , K. Uzun

In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term. For Schrodinger equation, we obtain the analytical expressions of the energies and the wave…

Quantum Physics · Physics 2019-11-05 M. Heddar , M. Moumni , M. Falek

We give one more proof in two and three space dimensions that the irregular solution of the Schrodinger equation, for zero angular momentum, is in fact the solution of an equation containing an extra 'delta function'. We propose another…

Quantum Physics · Physics 2007-05-23 Andre Martin

It is proved that when solving Schroedinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower dimensional cases. This…

Quantum Physics · Physics 2007-05-23 Zhao Wei-Qin

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…

Quantum Physics · Physics 2015-06-12 Huseyin Akcay , Ramazan Sever

The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…

Quantum Physics · Physics 2015-06-26 M. Kocak