The asymptotic iteration method for the eigenenergies of the anharmonic oscillator potential

The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

“…Recently a technique, called the Asymptotic Iteration Method (AIM) has been introduced [1,2] to obtain eigenvalues of second order homogeneous differential equations. In the case of the Schrödinger equation, it has been found that AIM exactly reproduces the energy spectrum for most exactly solvable potentials [2][3][4] and for non-exactly solvable potentials it produces very good results [5][6][7].…”

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

“…This method was applied by Barakat et al [25] to compute the angular spheroidal eigenvalues λ m ℓ (c) with real c 2 , and for the eigenenergies of the anharmonic oscillator potential [26]. The implementation of this method was straightforward, and the results were sufficiently accurate for practical purposes.…”

Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x) = Ax2α + Bx2

“…These two methods give the same results and closed to those already calculated by the AIM. 25 It is noteworthy that the relative error is less than 10 −4 . Figure 7 shows the variations of the normalized wave functions curves as function of position for the six first states and the potential V(x) = Ax 2α + Bx 2 with A=1, B=-4.9497 and α=3.…”

“…A variant of approximate methods and numerical techniques has recently been developed, [17][18][19][20][21][22][23][24] to calculate with high precision, the spectrum of one-dimensional symmetric anharmonic oscillators. Barakat 25 used the asymptotic iteration method (AIM) to calculate the eigen-energies for the anharmonic oscillator potentials V(x) = Ax 2α + Bx 2 , he introduced an adjustable parameter β to improve the AIM rate of convergence. However, the choice of the adjustment parameters is not usually simple.…”