Bound state solutions of D -dimensional schrödinger equation with exponential-type potentials (original) (raw)
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Physics Letters, 1994
We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene-Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.
Chinese Physics B, 2013
We study the D-dimensional Schrödinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of Jacobi polynomial. We also discussed two special cases of this potential comprises of the Hulthen potential and the Rosen-Morse potential in 3-Dimensions. Numerical results are also computed for the energy spectrum and the potentials, PACS Numbers: 03.65Ge, 03.65-w, 03.65Ca.
Bound-state solutions of the Schrödinger equation for central-symmetric confining potentials
Il Nuovo Cimento B, 1999
We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene-Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.
Bound State Solutions of the Schr\
Arxiv preprint arXiv:1012.1977, 2010
The effective mass one-dimensional Schrödinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the case of constant mass. Energy eigenvalues are computed numerically for some diatomic molecules. The results are in agreement with the ones obtained before.
New Solvable Potentials with Bound State Spectrum
Acta Physica Polonica B, 2017
A new family of solvable potentials related to the Schrödinger-Riccati equation has been investigated. This one-dimensional potential family depends on parameters and is restricted to the real interval. It is shown that this potential class, which is a rather general class of solvable potentials related to the hypergeometric functions, can be generalized to even wider classes of solvable potentials. As a consequence, the non-linear Schrödingertype equation has been obtained.
Pramana, 2012
The Nikiforov-Uvarov method is used to investigate the bound state solutions of Schrödinger equation with a generalized inverted hyperbolic potential in D-space. We obtain the energy spectrum and eigenfunction of this potential for arbitrary l-state in D dimensions. We show that the potential reduces to special cases such as Rosen-Morse, Poschl-Teller and Scarf potentials. The energy spectra and wave functions of these special cases are also discussed. The numerical results of these potentials are presented.
Solving the Schrödinger equation for bound states
Computer Physics Communications, 1985
Title ofprogram; SCR2 ments, scale transformation, numerical integration, convexity arguments, node theorem Catalogue number; ACDQ Nature of the physical problem Program obtainable from; CPC Program Library, Queen's Uni-SCR2 calculates energy levels and wave functions of the rotaversity of Belfast, N. Ireland (see application form in this issue) tional symmetric Schrodinger equation for a given potential using a simple and accurate method. Computer. VAX 11/750; Installation; Prozessrechenanlage Physik, Universität Wien Method ofsolution An iterative procedure for getting upper and lower bounds to Operating system; VMS 35 energy values of the radial Schrodinger equation is given. A numerical integration procedure together with convexity argu-Note; SCR2 runs also on the CDC CYBER 170/720 without ments and the nodal theorem for wave functions is used. modifications Typical running time Programming language u.sed. USANSI FORTRAN 77 5 s for one bound state. Note; The running time depends strongly on the desired accuracy. Program size; 2 Kbyte References No. of bits in a word; 32 [1) For applications see: H. Grosse and A. Martin, Phys. Rep. 60 (1980) 341. No. oflines in combinedprogram and test deck; 274 [2] M. Abramowitz and l.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968).
International Journal of Modern Physics C, 2009
We solve the Klein-Gordon equation in any D-dimension for the scalar and vector general Hulthén-type potentials with any l by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the calculations. We obtain the bound state energy eigenvalues and the corresponding eigenfunctions of spin-zero particles in terms of Jacobi polynomials. The eigenfunctions are physical and the energy eigenvalues are in good agreement with those results obtained by other methods for D = 1 and 3 dimensions. Our results are valid for q = 1 value when l = 0 and for any q value when l = 0 and D = 1 or 3. The s-wave (l = 0) binding energies for a particle of rest mass m 0 = 1 are calculated for the three lower-lying states (n = 0, 1, 2) using pure vector and pure scalar potentials.
The Analytical Solution of the Schr\"odinger Particle in Multiparameter Potential
arXiv (Cornell University), 2016
In this study, we present analytical solutions of the Schrödinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type approximation to the centrifugal potential. For any n and l (states) quantum numbers, we get the bound state energy eigenvalues numerically and the corresponding eigenfunctions.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.