Exact solution to the Lippmann-Schwinger equation for a spheroidal barrier

The flexibility in choosing distinct Green’s functions for the boundary wall method: waveguides and billiards

“…Taking into account the first relation in equation (17) for the successive integrals in equation (19), we get…”

“…Further conceptual aspects of the BWM have been examined in [18]. Also, the BWM is valid in any spatial dimension (see, e.g., [12,19]). The BWM has been employed in many distinct applications, as for the investigation of matter waves [20][21][22], analysis of diverse optical processes [23][24][25][26] and description of certain nanostructure properties [18,27,28].…”

“…We can cite straight lines [12] and circles [12,18], with this latter shape being recently revisited in terms of particular integral equation solution techniques applied to the BWM [16]. Moreover, a 2D elliptical billiard [17] (for numerics see [27]) and a 3D spheroidal barrier [19] have being analyzed through ingenious transformations and appropriate coordinate system choices for the BWM associated expressions. In all these cases, V is taken as the whole 2D or 3D space, thus with the polar or spherical symmetries of G 0 greatly complying with those of the investigated C's.…”

Quantum scattering by a spherical barrier with an arbitrary coupling strength

“…The keypoint is that a boundary-wall potential yields an LS equation with a separable kernel and this allows one to solve the equation analytically. We applied this methodology for scattering in two [17][18][19] and three-dimensions [20] and presented several analytical solutions of the LS equation.…”

“…this is a resonance effect which we studied in previous works considering circular, elliptic and spheroidal geometries [17,18,20]. On figure 2 on the left, we chose a wave number k such that j 3 (kR) = 0, where one would expect a resonance pattern to form and it is also possible to recognize the order and which zero was chosen, given the number of nodal lines present inside the barrier.…”