Bidimensional bound states for charged polar nanoparticles

Comment on: “Bidimensional bound states for charged polar nanoparticles”

“…After the Comment [3] and Reply [4] were published we could finally reproduce CC's results [1,4] by simply solving the eigenvalue equation for the Mathieu function as shown by Coïsson et al [5]. Table 2 shows a(ν) for q = 0.8147872 and ν = 1, 2, 3, 4.…”

“…Note that λ 0 (ξ) is negative for all ξ > 0. CC [1] chose a set of model parameters that appear to be suitable for (GaAs) 3 and obtained 4gp = 0.8147872. Table 1 shows that our results λ CC = 2λ for ξ = 0.8147872/8 do not agree with those in Table 1 of CC.…”

“…Boldface entries indicate the values of a(ν) reported by CC [1]. We conjecture that the algorithm used by those authors does not yield the eigenvalues orderly and for that reason they have been picking out the eigenvalues randomly which explains the discontinuity in CC's figure 1 [1] that does not appear in our more careful calculation given in figure 2 of our comment [3]. Figure 3 shows present results λ(ν) (blue, continuous line) and those given by CC [4] in their reply (red circles).…”

“…for the bound-states of the Schrödinger equation when λ ≥ 0 and E < 0 and some additional care is required for λ < 0. CC [1] bypassed the problem of negative eigenvalues λ m by postulating that they are physically unacceptable.…”

“…In a recent paper Castellanos-Jaramillo and Castellanos-Moreno [1] (CC from now on) put forward a simple quantum-mechanical model for an electron in the vicinity of an ionized nanostructure with a permanent electric dipole. They chose the interaction of the electron with the charge and the dipole in such a way that the resulting Schrödinger equation is separable into radial and angular parts.…”