The Schr ̈odinger equation is the fundamental equation in quantum physics. It defines a relationship between a particle’s energy and its wavefunction (related to probability). Through a series of calculations, one may approximately track the position of the particle. However, one may be interested in controlling the Schr ̈odinger equation by adjusting what is called the control term, such that two given states are satsified with the correct choice of the control. This idea proves useful where state controlling is crucial, such as quantum computing. In this thesis, a system of differential equations was derived that models position, dispersion, and the coined term “Ehrenfest Energy”. This was done to bring a system of infinite partially differential equations down to a finite system of ordinary differential equations. Through that system of differential equations, we provide approximations for each of the time dependent variables, including position. In addition, different control terms are applied in the hopes of understanding how the control term ultimately impacts the solution of position/dispersion. Lastly, we provide a series of plots demonstrating the difference between the quantum mechanical ‘measured’ position and the classical approach to measuring position

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