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We investigate the quantum dynamics of the forced harmonic oscillator and Jaynes-Cummings models. We find exact solutions for the time-evolution of the Jaynes-Cummings model using Wei-Norman factorization, and describe a technique that may be used to study time-dependent interaction strengths whose evolutions may not be analytically soluble. *This project was funded by the National Science Foundation under grant #1757998. To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.TSF.G01.20 

Control of quantum phenomena would allow for expanding control theory from classical systems to microscopic ones whose behavior is dictated by quantum mechanics. A current goal of quantum control is to develop a systematic methodology for the manipulation of systems. The approach typically used to solve dynamic quantum systems is useful to analyze characteristics of a system represented by a defined operator. The squeeze operator's actions are characterized by finding the time evolution operator using the Wei-Norman method on the associated Hamiltonian and applying this to number (Fock) states, coherent states, and Schrodinger cat states. This specific case analyzing the Squeeze operator shows that the Wei-Norman method to find time-evolution operator can reveal the dynamics of any system with an associated Lie Algebra basis. Documenting a variety of initial states and initial parameters in a library of cases provides a foundation to achieving greater control in experimental applications as well. *I would like to thank Brigham Young University for hosting this Research Experience for Undergraduates program and the National Science Foundation for funding this research through grant #1757998. To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.4CS.L04.6