The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Abstract

The generalized pseudospectral method is employed to calculate the bound states of Hulthén and Yukawa potentials in quantum mechanics, with special emphases on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a nonuniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with n ≤10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as up to n = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n > 6 states of Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of Yukawa potential, the present method surpasses in accuracy all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials. * Electronic address: akroy@unb.ca

Numerical solution of singular ODE eigenvalue problems in electronic structure computations

“…The number of elements in the point spectrum varies with α. Table 3 shows the results of our hybrid method and compares them to values reported in [26]. The most remarkable advantage of our approach is the high accuracy which is confirmed by a reliable a posteriori error estimate.…”

“…The next example we discuss is the Schrödinger equation with the Hulthén potential, which corresponds to (21)- (22) for V (r) = − αe −αr 1−e −αr [26]. Table 4 gives a comparison of our results with those from [26], where the displayed data corresponds with that in Table 3.…”

“…For further comparisons see [28]. Table 3: Example (21)- (22): Comparison of the eigenvalues of the Yukawa potential for several values of α reported in [26]. For the computations we prescribed tol a = 10 −15 and tol r = 10 −10 .…”

Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model

“…Noncentral potential in particular has been studied in various fields of nuclear physics and quantum chemistry which could be used for the interaction between deformed pair of nuclei and ring shaped molecules like benzenes [1][2][3][4][5]. Yukawa potential is one of the short ranged potentials that have been studied in physics, they have Coulombic behavior for small r and are exponentially damped for large r , and they have limited number of bound states characterized by the presence of the screening parameter α [6][7][8][9][10]. This model receives great attention for it plays an important role in high energy and particle physics, atomic physics, chemical physics, gravitational plasma physics and solid state physics.…”

Yukawa-angle Dependent Potential and its Applications to Diatomic Molecules under Schrodinger wave Equation

“…Yukawa potential is one of the short ranged potentials that have been studied in physics, they have coulombic behavior for small r and are exponentially damped for large r , and they have limited number of bound states characterized by the presence of the screening parameter α [6][7][8][9][10]. This model receives great attention due to the fact that it plays an important role in high energy and particle physics, atomic physics, chemical physics, gravitational plasma physics and solid state physics.…”