Comment on: “Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires” [Physica E 11 (2001) 345]

Flow-Acoustic Properties of Elliptic-Cylinder Waveguides and Enclosures

“…Specifically, we compare our modes in Figures 4 and 5 to their Figure 2. Note that the level ordering need not be the same if the eccentricities differ due to the phenomenon of level crossing [12]. Nevertheless, we find that, apart from one mode, we can relate our modes to theirs with the same ordering.…”

“…Related studies of waveguides and cavity resonators (including elliptic-cylinder geometries) play an essential role in microwave physics [7,8,9,10] as they are widely used in physical measurements and special devices. A recent examination of confined electronic states in flat elliptic semiconductor quantum dots and wires [11,12] emphasizes the interest in understanding wave propagation phenomena in ECC. Although, in the case with mean flow, the governing differential equation is different from the Helmholtz equation, it is still possible to separate the problem.…”

Electron energy spectra in an elliptic quantum wire and elliptic nanotube

“…As demonstrated in [10], generally the variables in Eq. (5) cannot be separated, because it is impossible to provide continuity of the wave function at the elliptic interface between the media.…”

“…Such solutions would be useful to study the energy spectrum of dimensional quasi-particle quantization in nanowires with asymmetric cross-sectional structure caused by uniaxial transverse deformation or conditions of nanostructure growth. However, as rightfully indicated in [10], solutions derived in [9] are exact only for an infinite potential barrier at the interface between media and for the ellipse degenerated into a circle. In [10] the electron energy spectrum in an elliptic quantum wire was obtained by numerical solution of the Schrödinger equation by the grid-point method, and its dependence on the ratio of semiaxes (а/b) was presented.…”

“…However, as rightfully indicated in [10], solutions derived in [9] are exact only for an infinite potential barrier at the interface between media and for the ellipse degenerated into a circle. In [10] the electron energy spectrum in an elliptic quantum wire was obtained by numerical solution of the Schrödinger equation by the grid-point method, and its dependence on the ratio of semiaxes (а/b) was presented. Unfortunately, the spectrum obtained in [10] was not compared with the results of [9] to estimate the accuracy of solutions [9] and to determine the field of their possible application.…”