Erratum to: “Analytical approximations to the solutions of the Manning–Rosen potential with centrifugal term” [Phys. Lett. A 368 (2007) 13]

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

“…Soylu et al [21] have obtained the analytical solutions of the Klein-Gordon equation for the equal scalar and vector Rosen-Morse potential and Eckart potential as well as parity-time symmetric version of these potentials by using the asymptotic iteration method. As mentioned above, the Manning-Rosen potential cannot be solved exactly for the arbitrary states except for an approximation to the centrifugal term [7,11,20]. However, It should be noted that the results obtained previously [7,11] are in good agreement with those obtained by using the program based on a numerical integration procedure [22] for the short-range potential, but the difference between them appears for the long-range potential.…”

“…As mentioned above, the Manning-Rosen potential cannot be solved exactly for the arbitrary states except for an approximation to the centrifugal term [7,11,20]. However, It should be noted that the results obtained previously [7,11] are in good agreement with those obtained by using the program based on a numerical integration procedure [22] for the short-range potential, but the difference between them appears for the long-range potential. Therefore, it is necessary and of considerable interest to find a new approximation approach to deal with the bound state and scattering state for Manning-Rosen potential.…”

“…For example, some authors have approximately solved the Schrödinger and Klein-Gordon equations for some po-tentials, these potentials include the Manning-Rosen potential [7], the Eckart potential [8], Hulthén potential [9], the Pöschl-Teller potential [10], etc. Based on previous work [7][8][9][10], we have applied a proper approximation to the centrifugal term to obtain approximately analytical −wave scattering solutions of the Schrödinger equation with the Manning-Rosen potential [11], the Eckart potential [12] and −wave bound solutions with the second Pöschl-Teller like potential [13] and the the hyperbolical potential [14] within the frame work of non-relativistic and relativistic quantum mechanics. The Manning-Rosen potential is an importantly solvable exponential-type potential describing diatomic molecules in quantum mechanics.…”

“…Therefore, it is necessary and of considerable interest to find a new approximation approach to deal with the bound state and scattering state for Manning-Rosen potential. Its expression is given by [7,11] …”

Energy States of Some Diatomaic Molecules: The Exact Quantisation Rule Approach

“…Few of these methods include the Feynman integral formalism [5,16], asymptotic iteration method (AIM) [1][2][3][4][5][17][18][19][20][21], functional analysis approach [22][23][24], exact quantization rule method [25][26][27][28][29][30][31][32][33], proper quantization rule [27,34], Nikiforov-Uvarov (NU) method [35][36][37][38], supersymetric quantum mechanics [40,[40][41][42][43][44][45], etc.…”