Exact time-evolution of a generalized two-dimensional quantum parametric oscillator in the presence of time-variable magnetic and electric fields

The time-dependent Schrödinger equation describing a generalized two-dimensional quantum parametric oscillator in the presence of time-variable external fields is solved using evolution operator method. For this, found as product exponential operators through Wei–Norman Lie algebraic approach. Then, propagator and time-evolution eigenstates coherent states are derived explicitly terms solutions to corresponding system coupled classical equations motion. In addition, formalism, we construct linear quadratic dynamical invariants that provide connection present results with those obtained via Malkin–Man’ko–Trifonov Lewis–Riesenfeld approaches. Finally, an exactly solvable model, introduce Cauchy–Euler type increasing mass decreasing frequency magnetic electric fields. Based on explicit for uncertainties expectations, squeezing properties wave packets their trajectories configuration space discussed according influence parameters