Phase-function method for velocity-dependent potentials

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

“…For instance, numerous authors have investigated the bound-state solutions of the Hulthen potential using various methods, including the Nikiforov-Uvarov (NU) method [19], the shifted 1/N expansion method [20], and the supersymmetry (SUSY) method [21][22][23][24], specifically for the s-wave Schrödinger equation. Furthermore, the Hulthen potential's solution has been obtained using the NU method and the Asymptotic Iteration Method (AIM) for relativistic wave equations, such as the Klein-Gordon equation [25][26][27][28][29][30][31][32], Dirac equation [33], and the Duffin-Kemmer-Petiau (DKP) equation [34]. Additionally, addressing the solutions for various angular momentum states of the Schrödinger equation for this potential has been accomplished in reference [35] through the application of AIM.…”

Analytical solution of the Schrödinger equation for isotropic velocity-dependent potentials

“…The effect of isotropic velocity-dependent potentials on the spectrum for any quantum states of different potentials has been studied analytically and approximately using different methods [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The quantum states of the Coulomb and harmonic oscillator potentials are calculated using the asymptotic iteration method [8]; the solution of the square well is obtained with the aid of the formal scattering theory [9,10].…”

“…The quantum states of the Coulomb and harmonic oscillator potentials are calculated using the asymptotic iteration method [8]; the solution of the square well is obtained with the aid of the formal scattering theory [9,10]. Furthermore, the perturbation theory [11,12], the asymptotic iteration method using Pekeris approximation [13,14], the phase-function method [15] and the path integration method [16] have been used to obtain the eigenvalues for some physical potentials.…”