Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension

Nyengeri, Hippolyte; Simbizi, René; Girukwishaka, Audace; Nizigiyimana, Rénovat; Ndenzako, Eugène

doi:10.4236/oalib.1104728

Cited by 2 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to obtain approximate analytical solution, a very suitable approximation scheme (Wei and Dong, 2010;Chen et al, 2009;Jia et al, 2008) must be applied on the spin-orbit term of the effective potential, having applied the approximation model on the centrifugal term, a solution method must be adopted to solve the resulting equation. Researchers have developed and used various solution methods to solve the Schrödinger equation, amongst some of the methods include: ansatz method (Taskin and Kocal, 2010), Nikiforov-Uvarov method (Ikot et al, 2014;Yazarloo et al, 2012), factorization method (Pahlavani et al, 2013), asymptotic iteration method (Awoga and Ikot 2012), Fröbenius series solution method (Nyengeri et al, 2018), exact quantization rule (Qiang et al 2008). Various forms of potential energy functions have been used to solve the radial Schrödinger equation.…”

Section: Introductionmentioning

confidence: 99%

Approximate ℓ-State Solution of Time Independent Schrödinger Wave Equation With Modified Möbius Squared Potential Plus Hulthén Potential

Dlama

E.S

Ibrahim

2020

FJS

View full text Add to dashboard Cite

In this work we have applied ansatz method to solve for the approximate ℓ-state solution of time independent Schrödinger wave equation with modified Möbius squared potential plus Hulthén potential to obtain closed form expressions for the energy eigenvalues and normalized radial wave-functions. In dealing with the spin-orbit coupling potential of the effective potential energy function, we have employed the Pekeris type approximation scheme, using our expressions for the bound state energy eigenvalues, we have deduced closed form expressions for the bound states energy eigenvalues and normalized radial wave-functions for Hulthén potential, modified Möbius square potential and Deng-Fan potential. Using the value 0.976865485225 for the parameter ω, we have computed bound state energy eigenvalues for various quantum states (in atomic units). We have also computed bound state energy eigenvalues for six diatomic molecules: HCl, LiH, TiH, NiC, TiC and ScF. The results we obtained are in near perfect agreement with numerical results in the literature and a clear demonstration of the superiority of the Pekeris-type approximation scheme over the Greene and Aldrich approximation scheme for the modified Möbius squares potential plus Hulthén potential.

show abstract

Section: Introductionmentioning

confidence: 99%

Approximate ℓ-State Solution of Time Independent Schrödinger Wave Equation With Modified Möbius Squared Potential Plus Hulthén Potential

Dlama

E.S

Ibrahim

2020

FJS

View full text Add to dashboard Cite

show abstract

“…It is well known that the exact solution of the Schrödinger Equation (SE) plays a vital role in quantum mechanics, and solving this equation is still an interesting work in the existing literature [1]- [6]. Generally, the SE is very difficult to solve for most physical central potentials [7] [8] [9].…”

Section: Introductionmentioning

confidence: 99%

“…Generally, the SE is very difficult to solve for most physical central potentials [7] [8] [9]. It is for this reason that approximation and numerical methods are frequently used to arrive at the solution [6] [10]- [15].…”

Section: Introductionmentioning

confidence: 99%

“…We have to add that the class of potentials under consideration contains all the approximation schemes of the orbital centrifugal term mentioned above. It also can be used to model the Gaussian potential well (GPW) through the expression [6] ( )…”

Section: Introductionmentioning

confidence: 99%

“…The Pöschl-Teller Polynomial PotentialAs another interesting special case of the class of potentials under consideration, we consider the potential of the form call "Pöschl-Teller polynomial potential" since it is a polynomial function in the PTP of the form = = . It has a very interesting aspect that it can be used to model the Gaussian function values of α , K and the j B coefficients[6]. In order to show that the potential(35) can have useful applications in physics, we study the three-dimensional SE for the attractive Gaussian potential de-…”

mentioning

confidence: 99%

See 2 more Smart Citations

Application of the Frobenius Method to the Schr？dinger Equation for a Spherically Symmetric Hyperbolic Potential

Nyengeri¹,

Nizigiyima²,

Ndenzako³

et al. 2018

OALib

Self Cite

View full text Add to dashboard Cite

In this paper, an efficient technique for computing the bound state energies and wave functions of the Schrödinger Equation (SE) associated with a new class of spherically symmetric hyperbolic potentials is developed. This technique is based on a recent approximation scheme for the orbital centrifugal term and on the use of the Fröbenius method (FM). The bound state eigenvalues are given as zeros of calculable functions. The corresponding eigenfunctions can be obtained by substituting the calculated energies into the recurrence relations for the expanding coefficients of the Fröbenius series representing the solution. The excellent performance of this technique is illustrated through numerical results for some special cases like Pöschl-Teller potential (PTP), Manning-Rosen potential (MRP) and Pöschl-Teller polynomial potential (PTPP), with an application to the Gaussian potential well (GPW). Comparison with other methods is presented. Our results agree noticeably with the previously reported ones.

show abstract

Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension

Cited by 2 publications

References 0 publications

Approximate ℓ-State Solution of Time Independent Schrödinger Wave Equation With Modified Möbius Squared Potential Plus Hulthén Potential

Approximate ℓ-State Solution of Time Independent Schrödinger Wave Equation With Modified Möbius Squared Potential Plus Hulthén Potential

Application of the Frobenius Method to the Schr？dinger Equation for a Spherically Symmetric Hyperbolic Potential

Contact Info

Product

Resources

About