@inproceedings{ca4c90e0ec984c599c7a45d4a402a356,

title = "Computer algebra in nanosciences: Modeling electronic states in quantum dots",

abstract = "In the present paper we discuss single-electron states in a quantum dot by solving the Schr{\"o}dinger equation taking into account spatial constraints, in which the confinement is modeled by a spherical potential wall (particle-in-a-sphere model). After the separation of variables we obtain second order ordinary differential equations, so that automatic methods for finding a closed-form solution are needed. We present a symbolic algorithm implemented in Maple based on the method of indeterminate coefficients, which reduces the obtained equations to the well-known differential equations. The latter can be solved in terms of hypergeometric or Bessel functions. The usage of indeterminate coefficients allows one to obtain the solution of the problem equations in terms of control parameters, which can then be choosen according to the purposes of a nanotechological process.",

author = "Dmytro Chibisov and Victor Ganzha and Sergey Pankratov and Christoph Zenger",

year = "2005",

doi = "10.1007/11555964_10",

language = "English",

isbn = "3540289666",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "115--124",

booktitle = "Computer Algebra in Scientific Computing - 8th International Workshop, CASC 2005, Proceedings",

note = "8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005 ; Conference date: 12-09-2005 Through 16-09-2005",

}