where m * ( x, ỹ) and V T ( x, ỹ) are only functions of x and ỹ due to the translational invariance along the z-axis. In the HADOKEN code, m * ( x, ỹ) is computed using the heaviside_core_schrod.m routine which is subsequently used as input as the "c" coefficient in the MATLAB PDE Toolbox pdeeig command. In addition, the HADOKEN code uses Dirichlet boundary conditions for Eq. ( ) where ψ n ( x, ỹ) is set to zero at the outer shell boundary to prevent any electron leakage outside the NW. The electrostatic potential energy, V( x, ỹ), satisfies Poisson's equation, which, in cgs units, is given by: