Approximate Bound States Solution of the Hellmann Potential

Hamzavi, Majid; Thylwe, Karl‐Erik; Rajabi, A. A.

doi:10.1088/0253-6102/60/1/01

Cited by 83 publications

(77 citation statements)

References 40 publications

(19 reference statements)

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“…They are in agreement with those of the previous results where we should also stress that our results are consistent with the ones given in Ref. [25]. Eq.…”

Section: Radial Solutionssupporting

confidence: 94%

“…The present potential could be used as a potential model for the alkali hydride molecules [20]. Energy eigenvalues of the Hellmann potential have recently been studied by various authors with the help of different methods such as 1/N expansion method [21], shifted large-N expansion method [22], the method of potential envelopes [23], the J -matrix approach [24] and the generalized Nikiforov-Uvarov method [25,26]. In the present work, we solve the Shrödinger-Hellmann problem in terms of the hypergeometric functions by using an approximation instead of the centrifugal term.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

PT-/non-PT-symmetric and non-Hermitian Hellmann potential: approximate bound and scattering states with anyℓ-values

Arda¹,

Sever²

2014

Phys. Scr.

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We investigate the approximate bound state solutions of the Schrödinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number ℓ.

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“…They are in agreement with those of the previous results where we should also stress that our results are consistent with the ones given in Ref. [25]. Eq.…”

Section: Radial Solutionssupporting

confidence: 94%

Section: Introductionmentioning

confidence: 99%

PT-/non-PT-symmetric and non-Hermitian Hellmann potential: approximate bound and scattering states with anyℓ-values

Arda¹,

Sever²

2014

Phys. Scr.

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“…The energy equation for these potentials were obtained in special cases. To test the accuracy of these results, we compared the result of Yukawa potential with the result of Hamzavi et al (2013) who used parametric NikiforovUvarov method. As it can be seen from the Table 2, our results are in good agreement with the previous result.…”

Section: Resultsmentioning

confidence: 99%

Application of formula method for bound state problems in Schrödinger equation

Ebomwonyi¹,

Onate²,

Odeyemi³

2019

Journal of Applied Sciences and Environmental Management

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By using Formula method for bound state problems, we have obtained the approximate analytical solution of the radial Schrӧdinger equation for Varshni potential model. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. In the process, eigen values for 1, 1, 2, a b a b = = = − = − and 1, 2 b a = − = − for 2 , 3 ,3 , 4 p p d p and 4 f states with three different values of the potential range were generated using the Varshni potential. Special cases of the potential are equally studied. Some numerical results have been presented which showed a good agreement with previous results obtained from another method.The study of exactly solvable problem has attracted much attention in theoretical physics since the development of quantum mechanics. For instance, the solutions of the non-relativistic Schrӧdinger equation for a hydrogen atom and a harmonic oscillator in three dimensions represent two typical examples in quantum mechanics (Schiff, 1955;Landau and Lifshitz, 1977). There are few traditional techniques or methods used to solve second-order differential equation in order to obtain the solutions of the quantum systems. These methods include Nikiforov-Uvarov method (Ebomwonyi et al., 2017; Ikot et al., 2015; Onate and Idiodi, 2015; Hamzavi and Ikhdair, 2012), asymptotic iteration method (Bayrak et al., 2007; Falaye et al., 2013; Bayrak and Boztosun, 2007; Ateser et al., 2007), supersymmetry shape invariance and solvable potential (Zarrinkamar et al., 2010; Jia et al., 2011; Hassanabadi, 2011; Onate et al., 2017), factorization method (Onyeaju et al., 2016), new exact quantization rule (Dong and Gonzalez-Cisneros, 2008; Gu et al., 2009) and others. Recently, Falaye et al. (2014) developed the Formula method for bound state problems from asymptotic iteration method. This method seems to be very effective, but the simplification in obtaining the energy equation is somehow technical; hence, resulting in little report on it in literature. This necessitates the present study; and in this paper, we intend to investigate the nonrelativistic Schrödinger equation with the Varshni potential function in the framework of the Formula method for bound state problems. To the best of our knowledge, this is the first time the Schrӧdinger equation is being studied with the Varshni potential function using the Formula method.The Varshni potential function is given as (Varshni, 1957;Oluwadare and Oyewumi, 2017) ( ) , r ab V a r e r δ − = −(1) Where, a and b are the potential strengths, δ is the screening parameter which controls the shape of the potential energy curve and r is the internuclear separation. The Varshni potential function is a short range repulsive potential energy function that plays an important role in both chemical and molecular physics (Varshni, 1957). The potential was used by Kaxiras and Pandey to describe the 2-body energy portion of multi-body condensed matter. This potential is used generally to describe bound states of the interaction of systems and has been applied in both...

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“…For`6 = 0 state, the Pekeris approximation type [2][3][4] have been used to obtain an approximate solutions. To obtain the bound state energy eigenvalues for any`state, various methods such as Asymptotic iteration method [5][6][7][8][9], Nikiforov-Uvarov method [10][11][12][13][14], exact quantization rule [15,16], shifted 1/N expansion method [17], supersymmetric method [18,19] have been used.…”

Section: Introductionmentioning

confidence: 99%