Quantum Mechanical Matrix Ordinary Differential Equations and Their Solutions by Characteristic Evolutions

摘要

In this work we show that a large class of second order matrix ordinary differential equations can be solved with the aid of an appropriate linear matrix ordinary differential equation whose solutions describe a motion we call "Characteristic Evolutions" as long as the accompanying initial conditions on the unknowns and their first derivatives possess some specific properties. The linear equations describing characteristic evolutions have a specific operator we call Hamiltonian which may have time variance depending on the structure of the matrix ODEs under consideration. In the derivation and utilization of what we obtain, recently developed "Fluctuation Free Matrix Representation" approximation is also used. Certain illustrative implementations for pretty simple cases where analytic solutions can be obtained are also given.