Solving Shrdinger Equations in Matrix Version
Yang Mou · Journal of Hefei Normal University · 2012
We present a basic and symmetric review on the matrix construction of Hamiltonian operators.The Hamiltonian matrices are usually obtained from finite difference method and the tight-binding model,the connection between which is discussed.Example calculation on a two-dimensional grid is given,and the wave-functions are analyzed for the comparison with the basic theory of quantum mechanics.The computational difficulties stemming from the huge dimension of matrix and the solution using computers is discussed.