Generalized Morse Potential Research Articles

From the generalized Morse potential to a unified treatment of the D-dimensional singular harmonic oscillator and singular Coulomb potentials

Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic oscillator and nonsingular Coulomb potentials in arbitrary dimensions with their additional accidental degeneracies are obtained as particular cases. Added bonuses from these mappings are the straightforward determination of the critical attractive singular potential, the proper boundary condition on the radial eigenfunction at the origin and the inexistence of bound states in a pure inversely quadratic potential.

A large class of bound-state solutions of the Schrödinger equation via Laplace transform of the confluent hypergeometric equation

It is shown that analytically soluble bound states of the Schrodinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent hypergeometric equation. It is also shown that all closed-form eigenfunctions are expressed in terms of generalized Laguerre polynomials. The generalized Morse potential is used as an illustration.

Analytical Solutions of the Fokker–Planck Equation for Generalized Morse and Hulthén Potentials

In the present contribution we analytically calculate solutions of the transition probability of the Fokker–Planck equation (FPE) for both the generalized Morse potential and the Hulthen potential. The method is based on the formal analogy of the FPE with the Schrodinger equation using techniques from supersymmetric quantum mechanics.

Exact Analytical Solution of theN-Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

The second-orderN-dimensional Schrödinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvaluesEnas a function of dimensionNare furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

A parametric approach to supersymmetric quantum mechanics in the solution of Schrödinger equation

We study exact solutions of the Schrödinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schrödinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.

Approximate -state solutions of the Dirac equation in spatially dependent mass for the Eckart potential including the Yukawa tensor interaction

We investigate the analytical approximation to arbitrary -state solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential including the Yukawa tensor interaction in the framework of a parametric Nikiforov–Uvarov method. By taking a proper approximation to deal with the centrifugal term, the analytical relativistic energy eigenvalues and the corresponding normalized two-spinor components of the wave function are obtained in closed form. The relativistic and non-relativistic bound state solutions for some special cases, such as the Hulthén potential and the generalized Morse potential, are easily obtained from our general solution.

Rigorous Study of the Unbinding Transition of Biomembranes and Strings from Morse Potentials

The purpose is an exact study of the unbinding transition from two interacting manifolds (strings or bilayer membranes). These systems have similar scaling behavior, and then it is sufficient to consider only the strings’ problem. We assume that the manifolds interact via a realistic potential of Morse type. To this end, the use is made of the transfer matrix method, based on the resolution of a Schrödinger equation. We first determine the associated bound states and energy spectrum. Second, the exact ground state energy gives the free energy density, from which we extract the expression of the unbinding temperature. Third, we determine the contact probability between manifolds, from which we compute the (diverging) average separation and roughness of the manifolds. It is found that their critical behavior is close to that obtained using Field-Theoretical Renormalization-Group. The conclusion is that these analytical studies reveal that the Morse potential is a good candidate for the study of the unbinding phenomenon within manifolds. Finally, the discussion is extended to generalized Morse potential.

Relativistic spin symmetry of the generalized Morse potential including tensor interaction

The relativistic Dirac equation under spin symmetry is investigated for generalized Morse potential. We calculated the eigenvalues and the corresponding wave function by using the Nikiforov-Uvarov method. We also discussed two special cases: attractive radial and Deng-Fan potentials. We have also reported some numerical results and figures to show the effect of tensor interaction.

Approximate Relativistic Bound State Solutions of the Tietz–Hua Rotating Oscillator for Any κ-State

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 exact spin and pseudo-spin (pspin) symmetric limitation, the bound state energy eigenvalues and associated two-component wave functions of the Dirac particle moving in the field of attractive and repulsive TH potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The cases of the Morse potential, the generalized Morse potential and non-relativistic limits are studied.

Approximate analytical solutions of a two-term diatomic molecular potential with centrifugal barrier

Approximate analytical bound state solutions of the radial Schr\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulth\'{e}n potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.

Bound State Solutions of Schrödinger Equation for Generalized Morse Potential with Position-Dependent Mass

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 constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry

By using an improved approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation for the generalized Morse potential with arbitrary spin-orbit quantum number κ. In the presence of spin and pseudospin symmetry, the analytic bound state energy eigenvalues and the associated upper- and lower-spinor components of two Dirac particles are found by using the basic concepts of the Nikiforov-Uvarov method. We study the special cases when κ = ±1 (\documentclass[12pt]{minimal}\begin{document}$l= \widetilde{l}=0,$\end{document}l=l̃=0, s-wave), the non-relativistic limit and the limit when α becomes zero (Kratzer potential model). The present solutions are compared with those obtained by other methods.

Approximate solutions of the Schrödinger equation with the generalized Morse potential model including the centrifugal term

AbstractBy using a new improved approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation with the generalized Morse potentials for the arbitrary angular momentum values. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method. The numerical experiments show that our approximate results are in better agreement with those obtained by using the numerical integration approach than the approximate results obtained by using the conventional approximation scheme to deal with the centrifugal term. We also calculate the rotational transition frequencies for HF molecule and compare them with the experimental data. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Effective-mass Klein–Gordon equation for non-PT/non-Hermitian generalized Morse potential

The one-dimensional effective-mass Klein–Gordon equation for the real, and non-PT-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. Energy eigenvalues and corresponding eigenfunctions are obtained. They are also calculated for the constant mass case.

Refined relationship between extended Rydberg and generalized Morse functions for a special class of diatoms

In line with the development of a potential function converter software, numerous relationships among parameters of interatomic potentials have been established in recent years. In the recently developed relationship between the extended Rydberg and the generalized Morse parameters an excellent agreement was found for a 2 > 0, but an inaccurate one for a 2 < 0. To address the inaccuracy of the latter case, a refined relationship is developed herein by recasting the generalized Morse potential in a form that more closely resembles the extended Rydberg function by using series approximation. Results show that, for the special case of a 2 < 0, the refined relationships give better agreement as compared to the previously developed one. Consequently, the developed relationship will be incorporated into the proposed potential function converter software.

Bound states of the Dirac equation with vector and scalar Eckart potentials

Solving the Dirac equation with equal Eckart scalar and vector potentials in terms of the supersymmetric quantum mechanics method, shape invariance approach and the function analysis method, we obtain the exact energy equation for the s-wave bound states. It has been shown that the energy equation and spinor wavefunction expressions for the Eckart potential include the energy equations and corresponding spinor wavefunctions for the Hulthén potential, generalized Morse potential and attractive radial potential.

Double shape invariance of the two-dimensional singular Morse model

A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part of the spectrum and corresponding wave functions, starting from one definite state, which can be obtained by the method of SUSY-separation of variables, proposed recently.

Two-dimensional SUSY-pseudo-Hermiticity without separation of variables

We study SUSY-intertwining for non-Hermitian Hamiltonians with special emphasis to the two-dimensional generalized Morse potential, which does not allow for separation of variables. The complexified methods of SUSY-separation of variables and two-dimensional shape invariance are used to construct particular solutions—both for complex conjugated energy pairs and for non-paired complex energies.

Light scattering from slightly rough semiconductor surfaces near exciton resonance

The phenomenon of light scattering by a randomly rough surface and fluctuations of the excitonic surface potential is investigated by means of a first-order perturbation theory. We employ the generalized Morse potential to describe both intrinsic (repulsive) potentials and extrinsic near-surface potential wells. Frequency and angle dependencies of the light-scattering cross section are calculated. A considerable increase of the scattering cross section, as the correlation between the surface roughness and the excitonic potential fluctuations diminishes, is observed. Our theory describes very well available experimental results for samples with a repulsive surface potential. Also, the optical manifestation of excitonic bound states, generated within a surface-potential well, is analyzed. We find that the near-surface localized excitons produce a resonance structure in the spectrum of the light-scattering cross section, which is very sensitive to the degree of correlation between surface roughness and potential-well fluctuations.

Connection between type A and E factorizations and construction of satellite algebras

Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and corresponding to different energy eigenvalues. Here the role of the factorization method in the construction of such algebras is investigated. A general procedure for determining an so(2,2) or so(2,1) satellite algebra for all the Hamiltonians that admit a type E factorization is proposed. Such a procedure is based on the known relationship between type A and E factorizations, combined with an algebraization similar to that used in the construction of potential algebras. It is illustrated with the examples of the generalized Morse potential, the Rosen-Morse potential, the Kepler problem in a space of constant negative curvature, and, in each case, the conserved quantity is identified. It should be stressed that the method proposed is fairly general since the other factorization types may be considered as limiting cases of type A or E factorizations.