Study of a bounded oscillator problem in one dimension

Çiftçi, Hakan; Ateser, Engin

doi:10.1088/0031-8949/76/5/019

Cited by 5 publications

(9 citation statements)

References 41 publications

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“…In this paper, the asymptotic iteration method (AIM), which has been proposed by Ciftci et al [34][35][36][37][38][39] in recent years, has been applied to solve the N-dimensional non-relativistic Schrödinger equation for diatomic molecules. This method of solution, based on solving the second-order homogeneous linear differential equations, has been used to solve one-, two-and three-dimensional Schrödinger equations for central potentials [38,[40][41][42]. The solutions of the Klein-Gordon equation with the generalized Hulten and Kratzer potential in D dimensions have been investigated with the AIM by Saad [43] and Saad et al [44], respectively.…”

Section: Introductionmentioning

confidence: 99%

Non-relativistic treatment of diatomic molecules interacting with a generalized Kratzer potential in hyperspherical coordinates

Durmus¹

2011

J. Phys. A: Math. Theor.

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We investigate solutions of a non-relativistic wave equation in hyperspherical coordinates for a diatomic molecule system interacting with a generalized Kratzer potential. Rovibrational eigenvalues and corresponding wavefunctions of non-relativistic diatomic molecules have been determined within the framework of the asymptotic iteration method. Certain fundamental conditions for the applications of the asymptotic iteration method, such as a suitable asymptotic form for the wave-function and the termination condition for the iteration process, are discussed. N-dimensional bound state eigenfunction solutions used in studying the dynamical variables of diatomic molecules are obtained in terms of a confluent hypergeometric function and a generalized Laguerre polynomial. This systematic approach is tested by calculating the rovibrational energy spectra of hydrogen and sodium chloride molecules.

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Section: Introductionmentioning

confidence: 99%

Non-relativistic treatment of diatomic molecules interacting with a generalized Kratzer potential in hyperspherical coordinates

Durmus¹

2011

J. Phys. A: Math. Theor.

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“…The use of 10 or 20 terms in the potential series instead of 2 or 3 caused no essential difficulty for the method, except that it became necessary to perform an extra check on the convergence of the results as the number of potential terms used was increased. Thus the method should also be applicable (at least for sufficiently large R values) to the potential x 2 /(1x 2 /R 2 ) 2 , which was treated by means of the AIM approach in a recent work [24].…”

Section: Discussionmentioning

confidence: 99%

A Hill-series approach to wavefunction nodes

Killingbeck¹

2009

J. Phys. A: Math. Theor.

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The Hill-series method is shown to have several advantages for treating the Schrödinger equation when the wavefunction obeys the Dirichlet boundary condition Ψ(R) = 0. A novel combination of the virial theorem, the Hill-series method and a finite difference method is used to find the node positions of the wavefunction for several excited states of perturbed oscillator and coulombic systems and to find critical radii for the hydrogen atom.

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“…The approach just mentioned was mainly applied to quantum-mechanical models with asymptotic boundary conditions at infinity [1][2][3][4][5][6][7][8][9][10][11], but it was suggested that it may be suitable for bounded problems as well [8]. In this paper, we try the RPM on the bounded anharmonic oscillator recently discussed by Ciftci and Ateser [12] that may be suitable for the study of quarkonium physics.…”

Section: Introductionmentioning

confidence: 99%

“…In secion 2, we outline the main features of the RPM. In section 3, we apply the RPM to the bounded oscillator proposed by Ciftci and Ateser [12]. In section 4, we briefly address the problem of spurious roots.…”

Section: Introductionmentioning

confidence: 99%