Exact solutions of the Schrodinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials

Arda, Altug
Sever, Ramazan
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrodinger 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 wave-functions 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.


Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules
IKHDAİR, SAMEER; Sever, Ramazan (Springer Science and Business Media LLC, 2009-04-01)
For arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D a parts per thousand yen 2) hyperradial Schrodinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact bound state energy eigenvalues (E (nl) ) are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (psi (nl) (r)) are also calculated. The exact energy eigenvalu...
Bound state solution of the Schrodinger equation for Mie potential
Sever, Ramazan; Bucurgat, Mahmut; TEZCAN, CEVDET; Yesiltas, Oezlem (Springer Science and Business Media LLC, 2008-02-01)
Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The bound states are calculated numerically for some values of l and n with n <= 5. They are applied to several diatomic molecules.
Legendrian realization in convex Lefschetz fibrations and convex stabilizations
Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01)
We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
An alternative series solution to the isotropic quartic oscillator in N dimensions
Taşeli, Hasan (Springer Science and Business Media LLC, 1996-01-01)
The series solution of the N-dimensional isotropic quartic oscillator weighted by an appropriate function which exhibits the correct asymptotic behavior of the wave function is presented. The numerical performance of the solution in Bill's determinant picture is excellent, and yields the energy spectrum of the system to any desired accuracy for the full range of the coupling constant. Furthermore, it converges to the well-known exact solution of the unperturbed harmonic oscillator wave function, when the an...
Bound states of a more general exponential screened Coulomb potential
Ikhdair, Sameer M.; Sever, Ramazan (Springer Science and Business Media LLC, 2007-05-01)
An alternative approximation scheme has been used in solving the Schrodinger equation to the more general case of exponential screened Coulomb potential, V(r) = -(a/r)[1 + (1 + br)e(-2br)]. The bound state energies of the 1s, 2s and 3s-states, together with the ground state wave function are obtained analytically upto the second perturbation term.
Citation Formats
A. Arda and R. Sever, “Exact solutions of the Schrodinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials,” JOURNAL OF MATHEMATICAL CHEMISTRY, pp. 971–980, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62661.