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L. Guechi

Publications and source records attributed to L. Guechi.

16 recordsLinked to original sources
arXiv2019

Path integral discussion of the improved Tietz potential 1

An improved form of the Tietz potential for diatomic molecules is \ discussed in detail within the path integral formalism. The radial Green's function is rigorously constructed in a closed form for different shapes of this potential. For $\left\vert q\right\vert \leq 1,$ and $\frac{1}{2α} \ln \left\vert q\right\vert 0$% , it is found that the quantization conditions are transcendental equations that requires numerical solutions. In the limit $q\rightarrow 0$, the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.

quant-ph↗
arXiv2019

Complete non-relativistic bound state solutions of the Tietz-Wei potential via the path integral approach

In this work, the bound state problem of some diatomic molecules in the Tietz-Wei potential with varying shapes is correctly solved by means of path integrals. Explicit path integration leads to the radial Green's function in closed form for three different shapes of this potential. In each case, the energy equation and the wave functions are obtained from the poles of the radial Green's function and their residues, respectively. Our results prove the importance the optimization parameter $c_{h}$ in the study of this potential which has been completely ignored by the authors of the papers cited below. In the limit $c_{h}\rightarrow 0$, the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.

quant-ph↗
arXiv2019

Approximate path integral solution for a Dirac particle in a deformed Hulthén potential

The problem of a Dirac particle moving in a deformed Hulthen potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a closed form for the Green's function of the second-order Dirac equation is done by using a proper approximation to the centrifugal term and the Green's function of the linear Dirac equation is calculated. The energy spectrum for the bound states is obtained from the poles of the Green's function. A Dirac particle in the standard Hulthen potential for q=1 and a Dirac hydrogen-like ion when q = 1 and a that tends to infinity are considered as particular cases.

quant-ph↗
arXiv2019

Comment on " Solutions of Dirac equation with an improved expression of the Rosen-Morse potential energy model including Coulomb-like tensor interaction"

The Nikiforov-Uvarov polynomial method employed by Aguda to solve the Dirac equation with an improved Rosen-Morse potential plus a Coulomb-like tensor potential is shown inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions and in each regime we show that the energy levels are determined by the solutions of a transcendental equation which can be solved numerically.

quant-ph↗
arXiv2019

Comment on " Approximate Analytical Versus Numerical Solutions of Schrödinger Equation Under Molecular Hua Potential "

We present arguments proving that the results obtained by Hassanabadi and coworkers in the study of the D-dimensional Schrödinger equation with molecular Hua potential through the supersymmetry method in quantum mechanics are incorrect. We identified the inconsistencies in their reasoning on the allowed values of the parameter q and we constructed the correct energy spectrum.

quant-ph↗
arXiv2017

Comment on "The Rotation-Vibration Spectrum of Diatomic Molecules with the Tietz-Hua Rotating Oscillator"

We present arguments demonstrating that the application of the Nikiforov-Uvarov polynomial method to solve the Schrödinger equation with the Tietz-Hua potential is valid only when $e^{-b_{h}r_{e}}\leq c_{h}<1$ and $r_{0}<r<+\infty $. In particular, it is pointed out that the numerical results with $c_{h}\neq 0$ for the diatomic molecules $\mathrm{HF}$, $\mathrm{N}_{2}$, $\mathrm{I}_{2}$, $\mathrm{H}_{2}$, $\mathrm{O}_{2}$ and $\mathrm{O}_{2}^{+}$ given in Tables 3-5 by Hamzavi and co-workers are wrong. When $-1\leq c_{h}<0$ or $0<c_{h}<e^{-b_{h}r_{e}}$, this approach is not suitable. In both cases, it is shown that the solutions of the Schrödinger equation are expressed in terms of the generalized hypergeometric functions $_{2}F_{1}\left( a,b,c;z\right) $. The determination of the energy levels requires the solution of transcendantal equations involving the hypergeometric function by means of the numerical procedure.

quant-ph↗
arXiv2015

Comment on "The spin symmetry for deformed generalized Pöschl-Teller potential"

In this comment, we show that the solutions of the-wave Dirac equation for deformed generalized Pöschl-Teller potential obtained by Wei et al are valid only for $q\geq1$ and $\frac{1}{2α}\ln{q}<r<\infty$. When $0<q<1$, we prove that the energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function. To test our results, the Morse potential is considered as limiting case.

math-ph↗
arXiv2015

Comment on "Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term"

It is shown that the application of the Nikiforov-Uvarov method by Ikhdair for solving the Dirac equation with the radial Rosen-Morse potential plus the spin-orbit centrifugal term is inadequate because the required conditions are not satisfied. The energy spectra given are incorrect and the wave functions are not physically acceptable. We clarify the problem and prove that the spinor wave functions are expressed in terms of the generalized hypergeometric functions. The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.

quant-ph↗
arXiv2003

Path integral treatment of a family of super-integrable systems in n-dimensional Euclidean space

The exact path integration for a family of maximally super-integrable systems generalizing the hydrogen atom in the $n$-dimensional Euclidean space is presented. The Green's function is calculated in parabolic rotational and spherical coordinate systems. The energy spectrum and the correctly normalized wave functions of the bound states are obtained from the poles of the Green's function and their residues, respectively.

quant-ph↗
arXiv2003

Algebraic treatment of super-integrable potentials

The so$(2,1)$ Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky-Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in $R^{2}.$ Among the super-integrable potentials in $R^{3}$, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced.

quant-ph↗
arXiv2003

Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS space

Explicit path integration is carried out for the Green's functions of special relativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowski space-time modeled by a Klein-Gordon particle in the universal covering space-time of the anti-de Sitter static space-time. The energy spectrum together with the normalized wave functions are obtained. In the non-relativistic limit, the bound states of the one- and three-dimensional ordinary oscillators are regained.

quant-ph↗
arXiv2003

On the path integration for the potential barrier $V_{0}\cosh ^{-2}(ωx)$

The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(ωx)$ is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for this potential into a path integral for the Morse potential problem. The dimensional extension technique is seen to be essential for performing the multiple integral representation of the propagator. The correctly normalized scattering wave functions and the scattering function are derived. To test the method employed, the free particle and the $δ-$function barrier are considered as limiting cases.

quant-ph↗
arXiv2002

Algebraic treatment of the confluent Natanzon potentials

Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined. Eventually, the three-dimensional harmonic potential, the three-dimensional Coulomb potential and the Morse potential may all be considered as particular cases.

quant-ph↗
arXiv2001

Path integral for a pair of time-dependent coupled and driven oscillators

The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized canonical transformations and without presupposing the knownledge of any auxiliary equation. The time-dependent oscillators system with an exponentially growing masses and coupling coefficient in time may be considered as particular case.

quant-ph↗
arXiv2001

Similarity transformations approach for a generalized Fokker-Planck equation

By using similarity transformations approach, the exact propagator for a generalized one-dimensional Fokker-Planck equation, with linear drift force and space-time dependent diffusion coefficient, is obtained. The method is simple and enables us to recover and generalize special cases studied through the Lie algebraic approach and the Green function technique.

physics.data-an↗