Analysis of Time Evolution Algorithms to be Utilized in Modeling Classical and Quantum Mechanical Systems*

Time evolution in classical and quantum mechanical systems has been the focus of research because the behavior of physical systems with time are determined by their initial conditions. Calculation methods for the system values as it changes throughout time have to be very accurate in order to have predictions that we can rely on. This is the challenge of time evolution and its modeling.

In this project several time evolution algorithms were implemented and evaluated according to criteria of accuracy, stability, and consistency. Several scalar algorithms were examined as well as a technique for matrix exponentiation. Results show that the matrix exponentiation technique has significant advantages and is suitable for use in extending the time evolution models for various systems.