Solvable model for three-dimensional quantum scattering of a particle off several separable interactions centred at n arbitrary points

Non-relativistic quantum scattering from non-local separable potentials: the eigenchannel approach

“…(5.1) and (5.2) is the special case of that proposed recently by de Prunelé [14] (see also [8]). As one can notice, for further simplicity the strengths of both spheres were taken to be equal and have value ω.…”

Size and Shape Effects on Electronic Energy Levels: From Infinite to Nanoscopic Systems in Three-Dimensional Space

“…(43) and (46) of Ref. [4]). The matrix b is defined by b ij z d ij À l j hx i j G 0 z jx j i where d ij is the Kronecker symbol, and the free resol-…”

“…[4]. The theoretical background is only briefly presented here with essentially the same notation as in [4].…”

“…As explained in [4], the bound state energies for a finite number of centres, or equivalently the poles on the negative real axis of the resolvent…”

“…We study this problem in the light of a recently proposed solvable model for the three-dimensional quantum scattering of a particle off several separable interactions [4]. Within this model, the atomic centres can be arranged in an arbitrary way in the three-dimensional space.…”