Narrow Results

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 m₀ = 1 are calculated for the three lower-lying states (n = 0, 1, 2) using pure vector and pure scalar potentials.

The non-Hermitian Hamiltonians of the type is solved for the generalized Hulthén potential in terms of Jacobi polynomials by using Nikiforov–Uvarov method. The exact bound-state energy eigenvalues and eigenfunctions are presented.

Approximate analytical solutions of Duffin–Kemmer–Petiau equation are obtained for a vector Hulthén potential. The solutions are reported for any J-state using an elegant approximation and methodology of supersymmetry quantum mechanics.

By using an improved new approximation scheme to deal with the centrifugal term, we investigate the bound state solutions of the Schrödinger equation with the Hulthén potential for the arbitrary angular momentum number. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our approximate analytical results are in better agreement with those obtained by using numerical integration approach for small values of the screening parameter δ than the other analytical results obtained by using the conventional approximation to the centrifugal term.

We developed a new and simple approximation scheme for centrifugal term. Using the new approximate formula for 1/r² we derived approximately analytical solutions to the radial Schrödinger equation of the Hulthén potential with arbitrary l-states. Normalized analytical wave-functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by C. S. Jia et al. and other methods such as the asymptotic iteration, the supersymmetry, the numerical integration methods and a Mathematica program, schroedinger, by W. Lucha and F. F. Schöberl.

We obtain the bound state energy eigenvalues and the corresponding wave functions of the Dirac particle for the generalized Hulthén potential plus a ring-shaped potential with pseudospin and spin symmetry. The Nikiforov–Uvarov method is used in the calculations. Contribution of the angle-dependent part of the potential to the relativistic energy spectra are investigated. In addition, it is shown that the obtained results coincide with those available in the literature.

We first revisit the nonrelativistic minimal length quantum mechanics and reveal an interesting symmetry of the problem. In fact, we will show that the cumbersome problem can be cast into the ordinary Schrödinger equation with a new effective potential. Next, as a typical example, we show the minimal length Schrödinger equation in the presence of a nonminimal Hulthén vector interaction. The transmission and reflection coefficients are reported as well.

The spinless Salpeter equation can be regarded as the eigenvalue equation of a Hamiltonian that involves the relativistic kinetic energy and therefore is, in general, a nonlocal operator. Accordingly, it is hard to find solutions of this bound-state equation by exclusively analytic means. Nevertheless, a lot of tools enables us to constrain the resulting bound-state spectra rigorously. We illustrate some of these techniques for the example of the Hulthén potential.

The analytical solution of the modified radial Schrödinger equation for the Hulthén potential is obtained within ordinary quantum mechanics by applying the Nikiforov–Uvarov method and supersymmetric quantum mechanics by applying the shape invariance concept that was introduced by Gendenshtein method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

In this paper, the analytical solutions of the $D$-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any $l$ orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary $l$ states for $D$-dimensional space.

In this work, we construct the analytical solution of the Schrödinger equation for a combined nuclear plus atomic Hulthén potential with different range parameters, using the Frobenius method. The atomic Hulthén potential acts as the screened Coulomb potential to represent the very short-range electromagnetic interaction. It is intended to emphasize how the impact of the combined potential in these situations is routinely examined within the context of nuclear physics. The Jost function is calculated from its integral representation in terms of the regular solution. From the phase of the Jost function, the scattering phase shifts for different partial waves, and further differential scattering cross-section and total cross-sections are calculated for alpha-proton and proton–proton systems. On comparing with the existing experimental data, we conclude that the results obtained are in close conformity with the previous works that exist in the literature.

The analysis of nucleon–nucleon elastic and inelastic scattering data is presented by considering the combined interaction of nuclear and electromagnetic potentials of equal range. The exact analytical off-shell solutions of the nonrelativistic Schrödinger equation for the effective potential with the centrifugal term are investigated using ordinary differential equation approach. Numerical results of scattering phase shifts, differential cross-sections and Transition matrices are in sensible conformity with previous works.

In this study, the analytical solutions of the Klein–Gordon equation for any $l$ states of the modified effective mass potential under the modified unequal scalar and vector Coulomb–Hulthén potential (MUSVCH-P) are derived by using an approximation method to the centrifugal potential term in the symmetries of relativistic noncommutative three-dimensional real space (RNC: 3D-RS). The new analytical expressions for eigenvalues of the energy spectrum and the new mass of mesons, such as charmonium and bottomonium that have the quark and antiquark flavor, have been estimated by using Bopp’s shift method, and perturbation theory. The energy state equation depends on the global parameters characterizing the noncommutativity space and the potential parameter $(v_0,s_0,v_1,s_1,m_0,m_1,\delta )$ in addition to the Gamma function and the discreet atomic quantum numbers $(j,l,s,m)$. The expression for the new energy spectra is applied to obtain the new mass spectra of heavy quarkonium systems (charmonium and bottomonium) in the symmetries of (RNC: 3D-RS). The comparisons show that our theoretical results are in very good agreement with the reported works.

In this paper, we present a complete solution for the problem of a relativistic particle without spin, of mass M and charge e, subject to linear combination of the Yukawa and Deformed Hulthén Potentials. In particular, we assess the radial Green’s function for the l states by introducing appropriate approximations of the terms (1/r) and (1/(r)). By choosing an appropriate spacetime transformation, the energy spectrum and the normalized wave functions of the bound states are obtained from the poles of Green’s function and its residues.