An Approach to Potential Scattering

Abstract

Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain.The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.

Equivalence of two alternative approaches to Schrödinger equations

“…Eqs. ( 4) and ( 5) are the concrete proof of the equivalence between the two alternative models appeared in [2,[6][7][8][9][10][11][12][13] and [14,15] for constant and non-constant mass cases, because for the above equations reduce to the well known equations with constant mass.…”

“…Further, this procedure has been used for the exact treatments of quantum states with nonzero angular momentum in the case where effective potentials have an analytical solution [6], for investigation of perturbed Coulomb interactions [7] and for a systematic search of exactly solvable non-central potentials [8]. The model is later extended to the scattering domain [9] deriving explicitly the changes in the partial wave phase shifts. Successful applications of the model to anharmonic oscillators and Yukawa type potentials are presented in [10] and [11], respectively.…”

“…Successful applications of the model to anharmonic oscillators and Yukawa type potentials are presented in [10] and [11], respectively. With the confidence gained from such applications involving constant mass, the model outlined is employed for the investigation of effective Hamiltonians with spatially varying mass in one dimension [12] and higher dimensions [13] leading to explicit expressions for the energy eigenvalues and eigenfunctions. These investigations have clarified the relation between exact solvability of the effective mass Hamiltonians in the literature and ordering ambiguity put forward due to the use of a position-dependent mass in equations.…”

“…These investigations have clarified the relation between exact solvability of the effective mass Hamiltonians in the literature and ordering ambiguity put forward due to the use of a position-dependent mass in equations. The model restricts naturally the possible choices of ordering and provides us an explicit comparison betweeen physically acceptable Hamiltonians [12,13].…”

“…Since in this paper, only 1) should be maintained. The substitution of (x) = f (x)F [g(x)] in the most favourable one-dimensional time-independent Schrödinger equation [12,13,17] associated with a particle endowed with a position-dependent effective mass…”