Quantum Many-Body System with Variable Effective Mass in Presence of Time-Dependent Relative Harmonic Interactions and Electric Filed

In this article, a quantum many body system is considered. Then two time-dependent interactions have been added to the system. Changing of the interactions are assumed in general form. After that, by using algebraic method, time evolution of this many body system is investigated. In order to study the time evolution, Lewis-Riesenfeld dynamical invariant and time evolution operator method have been used. Appropriate dynamical invariants are constructed and their Eigen values are derived as well as appropriate time evolution operators are constructed. At the end, a comparison has been done between the derived results in the article considering a special case.