Schrödinger State Space Matrix Parametres Estimation

The Schrödinger equation as a quantum superposition describes the atomic orbital as a linear difference functions basis set. Another alternative is that this equation could be written as a m-dimensional state space linear stochastic system with unknown matrix coefficients with smooth movements around the stationary region. Thus, the matrix is estimated in a probability sense considering the distribution function and its stochastic moments. The matrix estimation result is an alternative solution without losing the general system properties. The estimation is based on a gradient stochastic technique with an instrumental variable such that the contribution matrix is optimal in a probability sense. Therefore, the advantages with respect to traditional solutions are focused on estimating the matrix contribution on-line with a linear complexity.