Exact solutions of the Schrodinger equation with non central potential by Nikiforov Uvarov method

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 eigenvalues and eigenfunctions for these potentials are derived analytically. Non central potential is reduced to Coulomb and Hartmann potential by making special selections, and the obtained solutions are compared with the solutions of Coulomb and Hartmann ring shaped potentials given in literature.Comment: 12 pages. submitted to Journal of Physics A: Math. and Ge

A search on the Nikiforov-Uvarov formalism

An alternative treatment is proposed for the calculations carried out within the frame of Nikiforov-Uvarov method, which removes a drawback in the original theory and by pass some difficulties in solving the Schrodinger equation. The present procedure is illustrated with the example of orthogonal polynomials. The relativistic extension of the formalism is discussed.Comment: 10 page

First-principles investigation of pentagonal and hexagonal core-shell silicon nanowires with various core compositions

Properties of various core-shell silicon nanowires are investigated by extensive first-principles calculations on the geometric optimization as well as electronic band structures of the nanowires by using pseudopotential plane-wave method based on the density-functional theory. We show that different geometrical structures of silicon nanowires with various core compositions, formed by stacking of atomic polygons with pentagonal or hexagonal cross sections perpendicular to the wire axis, can be stabilized by doping with various types of semiconductor (Si, Ge), nonmetal (C), simple metal (Al), and transition metal (TM), 3d (Ti, Cr, Fe, Co, Ni, Cu), 4d (Nb, Mo, Pd, Ag), and 5d (Ta, W, Pt, Au), core atoms. Dopant atoms are fastened to a linear chain perpendicular to the planes of Si-shell atoms and are located through the center of planes. According to the stability and energetics analysis of core-shell Si nanowires, the eclipsed pentagonal and hexagonal structures are energetically more stable than the staggered ones. Electronic band structure calculations show that the pentagonal and hexagonal Si-shell nanowires doped with various different types of core atoms exhibit metallic behavior. Magnetic ground state is checked by means of spin-polarized calculations for all of the wire structures. The eclipsed hexagonal structure of Si-shell nanowire doped with Fe atom at the core has highest local magnetic moment among the magnetic wire structures. Electronic properties based on band structures of Si-shell nanowires with different dopant elements are discussed to provide guidance to experimental efforts for silicon-based spintronic devices and other nanoelectronic applications. © 2009 The American Physical Society

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.Comment: 18 page

Effective Mass Dirac-Morse Problem with any kappa-value

The Dirac-Morse problem are investigated within the framework of an approximation to the term proportional to $1/r^2$ in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov-Uvarov method for any $\kappa$-value. It is also studied the approximate energy eigenvalues, and corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.Comment: 12 page

Path integral solution for an angle-dependent anharmonic oscillator

We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we were able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.Comment: Corrected typos and mistakes, To appear in Communications in Theoretical Physic

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of the two Dirac particles are obtained, in closed form, by means of the Nikiforov-Uvarov method which is based on solving the second-order linear differential equation by reducing it to a generalized equation of hypergeometric type. The special cases $\kappa =\pm 1$ ($l=\widetilde{l}=0,$ s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. Also, the non-relativistic results are compared with the other works.Comment: 25 page

Dirac Equation with Spin Symmetry for the Modified P\"oschl-Teller Potential in DD-dimensions

We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtain are in terms of the Jacobi polynomials. It is found that there exist only positive-energy states for bound states under spin symmetry, and the energy levels increase with the dimension and the potential range parameter $\alpha$.Comment: 9 pages and 1tabl

Exact solutions of the radial Schrodinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.Comment: 13 page

Direct exfoliation and dispersion of two-dimensional materials in pure water via temperature control

The high-volume synthesis of two-dimensional (2D) materials in the form of platelets is desirable for various applications. While water is considered an ideal dispersion medium, due to its abundance and low cost, the hydrophobicity of platelet surfaces has prohibited its widespread use. Here we exfoliate 2D materials directly in pure water without using any chemicals or surfactants. In order to exfoliate and disperse the materials in water, we elevate the temperature of the sonication bath, and introduce energy via the dissipation of sonic waves. Storage stability greater than one month is achieved through the maintenance of high temperatures, and through atomic and molecular level simulations, we further discover that good solubility in water is maintained due to the presence of platelet surface charges as a result of edge functionalization or intrinsic polarity. Finally, we demonstrate inkjet printing on hard and flexible substrates as a potential application of water-dispersed 2D materials.close1