Symmetric matrix methods for Schrodinger eigenvectors
Brian Grieves, Dennis Dunn · Journal of Physics A Mathematical and General · 1990
The one-dimensional single-particle Schrodinger eigenvalue equation is represented by a generalized matrix eigenvalue equation of the form A Psi =Ea Psi where A is a symmetric matrix, a is a symmetric positive-definite matrix and Psi is a column vector. The local error in making the representation is proportional to delta 4 where delta is the step size. Several methods of solution which make use of the sparsity of the matrices are investigated.