Modified l-states of diatomic molecules subject to central potentials plus an angle-dependent potential

We present modified $\ell$-states of diatomic molecules by solving the radial and angle-dependent parts of the Schr\"odinger equation for central potentials, such as Morse and Kratzer, plus an exactly solvable angle-dependent potential $V_{\theta}(\theta)/r^2$ within the framework of the Nikiforov-Uvarov (NU) method. We emphasize that the contribution which comes from the solution of the Schr\"odinger equation for the angle-dependent potential modifies the usual angular momentum quantum number $\ell$. We calculate explicitly bound state energies of a number of neutral diatomic molecules composed of a first-row transition metal and main-group elements for both Morse and Kratzer potentials plus an angle-dependent potential.Comment: 19 page

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.Comment: 13 page

Bound State Solutions of the Schr\"odinger Equation for Generalized Morse Potential With Position Dependent Mass

The effective mass one-dimensional Schr\"odinger 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.Comment: Accepted for publication in Commun. Theor. Phys., 12 pages, 1 tabl

Exponential Type Complex and non-Hermitian Potentials within Quantum Hamilton-Jacobi Formalism

PT-/non-PT-symmetric and non-Hermitian deformed Morse and Poschl-Teller potentials are studied first time by quantum Hamilton-Jacobi approach. Energy eigenvalues and eigenfunctions are obtained by solving quantum Hamilton-Jacobi equation.Comment: 16 page

Feinberg-Horodecki Equation with P\"oschl-Teller Potential: Space-like Coherent States

We obtain the quantized momentum solutions, $\mathcal{P}_{n}$, of the Feinberg-Horodecki equation. We study the space-like coherent states for the space-like counterpart of the Schr\"odinger equation with trigonometric P\"oschl-Teller potential which is constructed by temporal counterpart of the spatial P\"oschl-Teller potential.Comment: 8 page

Exact Solutions of the Schr\"odinger Equation via Laplace Transform Approach: Pseudoharmonic potential and Mie-type potentials

Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wavefunctions of the above potentials. It is also given numerical results for the bound states of two diatomic molecular potentials, and compared the results with the ones obtained in literature.Comment: 15 pages, 2 figure

Approximate analytical solutions of the Dirac equation for Yukawa potential plus Tensor Interaction with any κ\kappa-value

Approximate analytical solutions of the Dirac equation are obtained for the Yukawa potential plus a tensor interaction with any $\kappa$-value for the cases having the Dirac equation pseudospin and spin symmetry. The potential describing tensor interaction has a Yukawa-like form. Closed forms of the energy eigenvalue equations and the spinor wave functions are computed by using the Nikiforov-Uvarov method. It is observed that the energy eigenvalue equations are consistent with the ones obtained before. Our numerical results are also listed to see the effect of the tensor interaction on the bound states.Comment: 15 page