類氫雜質在有限位能阱量子點中的能階與波函數的特性

Abstract

In this thesis we study the eigenenergy and eigenstate of HydrogenicImpurity in a space having only one Quantum Dot which potential is finite.From a sphere finite potential Quantum Dot, we study the change of eigenenergy and eigenfunction by (1)change the shape (2)change the size(3)change the position of the hydrogenic impurity on rotation-symmetry axis(4)change thepotential value (5)move the hydrogenic impurity outside the Quantum dot (6)some special case like egg like and distribution of potential is parabolic (1~5 is equal-potential and change to other value on boundary). The calculation method used in our work is based on the theory proposedby Gorecki and Brown in 1989. We extend the original ideal of Gorecki and Brown to include more basis functions to evaluate the eigenenergy and eigenfunctions and that it to converge more fast , and let it can calculate the question of finite potential and also can evaluate the potential is nota step function or change it's shape to other kind (not only sphere and ellipse). By the forte, we can threat the problenm which others never consider before, for example, egg like and parabolic potential .