Approximate analytical solutions of the relativistic equations with the Deng–Fan molecular potential including a Pekeris-type approximation to the (pseudo or) centrifugal term
Abstract:By employing the Pekeris-type (or a new improved approximation) to deal with the (pseudo or) centrifugal term, we solve the Klein–Gordon and Dirac equations with equally mixed scalar and vector Deng–Fan molecular potentials for all values of l (orbital the angular momentum quantum number) and κ (spin–orbit coupling quantum number), respectively. Using the formalism of the Nikiforov–Uvarov method, the approximate analytical bound state energy equations and the associated two-component spinors corresponding to t… Show more
“…where σ(z) and σ(z) are polynomials, at most second degree, and τ (z) is a polynomial of first degree [31,39,40,51,57,73,74,93,98,99,102,104,103,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122].…”
Section: Appendix a The Nikiforov-uvarov Methodsmentioning
confidence: 99%
“…This potential has been widely studied by some researchers in various applications [65,66,67,68,69,70,71,72,73,74,75]. This potential model can be used to describe the motion of the nucleons in the mean field produced by the interactions between nuclei [65].…”
By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schrödinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.
“…where σ(z) and σ(z) are polynomials, at most second degree, and τ (z) is a polynomial of first degree [31,39,40,51,57,73,74,93,98,99,102,104,103,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122].…”
Section: Appendix a The Nikiforov-uvarov Methodsmentioning
confidence: 99%
“…This potential has been widely studied by some researchers in various applications [65,66,67,68,69,70,71,72,73,74,75]. This potential model can be used to describe the motion of the nucleons in the mean field produced by the interactions between nuclei [65].…”
By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schrödinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.
“…27 The Pekeris approximation approach has been widely used to investigate the analytical solutions of the Klein-Gordon equation with various molecular potential models. [11][12][13] We replace the centrifugal potential energy term by the following form…”
“…Schrodinger equation forms the non-relativistic part of the quantum mechanics and obtaining both exact and arbitrary solution with some chosen potentials has been of great interest because of its enormous applications [1][2] Obtaining the total wave function and its corresponding eigen value is essential and very important as its provides the necessary information for the quantum mechanical systems [3][4][5]. Many authors have provided both exact and approximate solutions to Schrodinger equation using different solvable potentials such as Pseudoharmonic, Rosen-Morse, coulomb , Yukawa, Kratzer ,Hellmann potentials [6][7][8][9].…”
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy eigen value and its associated total wave function . This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter. The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1) shows the different energy levels for a particular quantum number.
KEYWORDSSchrodinger, Nikiforov-Uvarov method, Woods-Saxon potential plus modified exponential potential.
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