| 1. |
- Belov, Sergey, et al.
(författare)
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On Regge pole trajectories for a rational function approximation of Thomas-Fermi potentials
- 2010
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 43:36, s. 365301-
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Tidskriftsartikel (refereegranskat)abstract
- The positions of two Regge poles caused by the rational function approximate Thomas-Fermi potential (a screened attractive Coulomb potential) are studied in detail as a function of the scattering energy. The leading pole is traced from the right-hand (physical) complex angular momentum plane K(l) > - 1/2 to the left-hand (unphysical) complex angular momentum plane K(l) < - 1/2 as the scattering energy is increased indefinitely. The second Regge pole is located in the unphysical half-plane at all energies. In this study an exact numerical and an approximate semiclassical WKB methods are discussed in some detail, where the boundary conditions of the regular (physical) Schrodinger solution become important. Transitions in behavior of Regge poles are explained in terms of Stokes lines and turning points evolution. The major change in the direction of Regge trajectories is demonstrated as a transition in the topology of Stokes lines. This phenomenon is caused by switching from one pair of turning points to another pair as the third turning point approaches the Stokes line connecting to the original turning points.
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| 2. |
- Hamzavi, M., et al.
(författare)
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Approximate analytical solution of the yukawa potential with arbitrary angular momenta
- 2012
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Ingår i: Chinese Physics Letters. - 0256-307X .- 1741-3540. ; 29:8, s. 080302-
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Tidskriftsartikel (refereegranskat)abstract
- The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.
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| 3. |
- Hamzavi, M., et al.
(författare)
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Approximate Bound States Solution of the Hellmann Potential
- 2013
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Ingår i: Communications in Theoretical Physics. - : IOP Publishing. - 0253-6102 .- 1572-9494. ; 60:1, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- The Hellmann potential, which is a superposition of an attractive Coulomb potential -a/r and a Yukawa potential b e(-delta r)/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrodinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.
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| 4. |
- Hamzavi, M., et al.
(författare)
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Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules
- 2013
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Ingår i: Journal of Mathematical Chemistry. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 51:1, s. 227-238
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Tidskriftsartikel (refereegranskat)abstract
- We obtain the bound-state solutions of the radial Schrodinger equation with the shifted Deng-Fan oscillator potential in the frame of the Nikiforov-Uvarov method by employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding normalized wave functions are obtained in closed form for arbitrary l-state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.
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| 5. |
- Hamzavi, M., et al.
(författare)
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Pseudospin symmetry in the relativistic Killingbeck potential : Quasi-exact solution
- 2012
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Ingår i: Zeitschrift fur Naturforschung A-A Journal of Physical Sciences. - 0932-0784 .- 1865-7109. ; 67:10-11, s. 567-571
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Tidskriftsartikel (refereegranskat)abstract
- The Killingbeck potential consisting of the harmonic oscillator plus Cornell potential, ar2 +br-c/r, is of great interest in particle physics. The solution of the Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin (p-spin) symmetry within the context of quasiexact solutions. Two special cases of the harmonic oscillator and Coulomb potential are also discussed.
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| 6. |
- Hamzavi, M., et al.
(författare)
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Spin and pseudospin symmetries in relativistic trigonometric Pöschl-teller potential with centrifugal barrier
- 2012
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Ingår i: International Journal of Modern Physics E. - 0218-3013. ; 21:12, s. 1250097-
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Tidskriftsartikel (refereegranskat)abstract
- Approximate analytical solutions of the Dirac equation with the trigonometric Pöschl-Teller (tPT) potential are obtained for arbitrary spin-orbit quantum number κ using an approximation scheme to deal with the spin-orbit coupling terms κ(κ±1)r-2. In the presence of exact spin and pseudo-spin (p-spin) symmetric limitation, the bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle moving in the field of attractive and repulsive tPT potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The case of nonrelativistic limit is studied too.
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| 7. |
- Hamzavi, M., et al.
(författare)
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Spinless particles in the field of unequal scalar-vector Yukawa potentials
- 2013
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Ingår i: Chinese Physics B. - : IOP Publishing. - 1674-1056. ; 22:4, s. 040301-
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Tidskriftsartikel (refereegranskat)abstract
- We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mixture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG-Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2-6.
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| 8. |
- Hamzavi, M., et al.
(författare)
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The rotation-vibration spectrum of diatomic molecules with the tietz-hua rotating oscillator
- 2012
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Ingår i: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608 .- 1097-461X. ; 112:15, s. 2701-2705
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Tidskriftsartikel (refereegranskat)abstract
- The Tietz-Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov-Uvarov method, we have obtained the exact analytical s-wave solutions of the radial Schrodinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented.
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| 9. |
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| 10. |
- Linnaeus, I. Jakusjina, et al.
(författare)
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Doubly uniform semiclassical quantization formula for resonances
- 2009
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Ingår i: European Physical Journal D. - : Springer Science and Business Media LLC. - 1434-6060 .- 1434-6079. ; 53:3, s. 283-288
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Tidskriftsartikel (refereegranskat)abstract
- The radial Schrodinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point. Numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of 'exact' numerical computations. The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero.
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