Spectral convergence of the Hermite basis function solution of the Vlasov equation: The free-streaming term

In this paper a new algorithm is presented for calculating the Green’s function of the Schrödinger equation in the presence of block layered potentials. Such Green’s functions have various and practical applications in quantum modelling of electron transport within nano-MOSFET transistors. The proposed method is based on expansions of the eigenfunctions of the subordinate Sturm–Liouville problems and a collocation matching procedure along possibly curved interfaces of the potential blocks. Accurate numerical results are provided to validate the proposed algorithm.