Exact solution of Schrödinger equation for Pseudoharmonic potential

Sever, R.; Tezcan, Ç.; Aktaş, Meti̇n; Yesiltas, Oezlem

doi:10.1007/s10910-007-9233-y

Cited by 64 publications

(90 citation statements)

References 37 publications

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“…Using (46,47), we calculate energy eigenvalues and the corresponding wave functions as From (26) and (38), we obtain the parameters (α 1 − α 13 ) and (ξ 1 − ξ 3 ) so energy eigenvalues become…”

Section: Nikiforov-uvarov Methodsmentioning

confidence: 99%

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A General Approach for the Exact Solution of the Schrödinger Equation

2008

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Section: Nikiforov-uvarov Methodsmentioning

confidence: 99%

“…These potentials are Morse [41], Rosen-Morse [42][43][44], Pseudoharmonic [45,46], Mie [47][48][49][50][51][52][53][54], Woods-Saxon [55][56][57][58][59][60][61], Poschl-Teller [62][63][64][65][66], Kratzer-Fues [67,68], Noncentral [69][70][71][72]. Woods-Saxon potential describes the interaction of a neutron with a heavy nucleus.…”

Section: Introductionmentioning

confidence: 99%

A General Approach for the Exact Solution of the Schrödinger Equation

2008

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“…We solve the D-dimensional PDEM Schrödinger equation exactly for two potentials: the pseudoharmonic potential [26][27][28][29][30][31] and the modified Kratzer molecular potential [32][33][34][35][36][37]. The transformation function g(r) will be found for the given effective mass function m(r) = m 0 r λ and the selected PCT function q(r) = r ν .…”

Section: Methodsmentioning

confidence: 99%

“…In this work, we employ the PCT to solve the D-dimensional Schrödinger equation with PDEM for the pseudoharmonic [26][27][28][29][30][31] and modified Kratzer [32][33][34][35][36][37] potentials through mapping this wave equation into the well-known exactly solvable D-dimensional Schrödinger equation with constant mass for a given PDEM function [1]. Indeed, the PCT approach has enabled us to obtain the exact effective mass bound state solutions including the energy spectrum and corresponding wave functions in any dimension for the exactly solvable classes of quantum molecular potentials.…”

Section: Introductionmentioning

confidence: 99%

Exactly Solvable Effective Mass D-Dimensional Schrödinger Equation for Pseudoharmonic and Modified Kratzer Problems

Ikhdair

Sever

2009

Int. J. Mod. Phys. C

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“…Solutions of Schrödinger equation for some physical potential have important applications in molecular physics, quantum chemistry, nuclear, condensed matter physics, high energy physics and particle physics. These potentials are such as, Hulthén [1], Morse [2], RosenMorse [3], Pseudo-harmonic [4], Mie [5], Poschl-Teller [6], Kratzer-Fues [7] and Woods-Saxon [8]. We usually solve these potentials as analytically and we can calculate energy eigenvalues and the corresponding wave functions exactly.…”

Section: Introductionmentioning

confidence: 99%

Determined position dependent Mass of the Rosen-Morse potential and its Bound state

Amani

2015

J. Phys.: Conf. Ser.

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Abstract. In this paper, Schrödinger equation has been solved analytically with position dependent mass by the Rosen-Morse potential. The position dependent mass defined as the function 1/(1 − tanh(ηx)). Then corresponding position dependent mass substituted into Schrödinger equation. After that the obtained equation compared with associated Jacobi differential equation. Therefore, the eigenvalue and eigenfunction have been calculated, and from there the bound state has been found in terms of quantum numbers and the coefficients of potential. Also, the wave function has been obtained in terms of the associated Jacobi equation by µ = −3 and ν = 2. IntroductionOne of the fundamental wave equations is the Schrödinger equation that one used in physics and chemistry. Solutions of Schrödinger equation for some physical potential have important applications in molecular physics, quantum chemistry, nuclear, condensed matter physics, high energy physics and particle physics. These potentials are such as, and Woods-Saxon [8]. We usually solve these potentials as analytically and we can calculate energy eigenvalues and the corresponding wave functions exactly. Application of the mentioned potentials and Woods-Saxon potential are very useful to describe molecular structures and the interaction of a neutron with a heavy nucleus, respectively.Exact solutions of Schrödinger equation for the mentioned potentials are interesting in the fields of material science and condense matter physics. We note that, there are various methods to obtain exact solutions energy eigenvalues and corresponding wave function. One of the methods is a factorization method that can factorize the Hamiltonian of corresponding system in terms of production of two first order differential operators, in which so-called lowering and raising operators. The two obtained Hamiltonian are partner of each other. This method allowed to classify the problems according to the characteristics involved in the potentials and it is closely related to the supersymmetric quantum mechanics [9,10,11].In quantum mechanics, all of the analytically solvable potentials have a feature that be called as shape invariance. In fact, the shape invariance is an integrability condition and an interesting feature of supersymmetric quantum mechanics. This method is an exact and elegant technique to determine the eigenvalues and eigenfunctions of quantum mechanical problems [9].

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Exact solution of Schrödinger equation for Pseudoharmonic potential

Cited by 64 publications

References 37 publications

A General Approach for the Exact Solution of the Schrödinger Equation

A General Approach for the Exact Solution of the Schrödinger Equation

Exactly Solvable Effective Mass D-Dimensional Schrödinger Equation for Pseudoharmonic and Modified Kratzer Problems

Determined position dependent Mass of the Rosen-Morse potential and its Bound state

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