The main objective of this book is to explore the effects to continuous, unsharp measurements on a single quantum particle and the effects of applying feedback to the system. We consider the particle to be free in some cases, and trapped in a harmonic potential in others, in order to get an idea of the different dynamics. It is found that the different dynamics produces fascinating, asymptotic, steady state solutions with interesting links between the free particle and trapped particle cases.As an introduction to the methods of unsharp measurements, the reader is taken through sections involving the Standard Quantum Limit (SQL) [1] where variances are calculated using unsharp measurements. Once the necessary back-ground theory is covered, the reader is guided through more interesting scenarios. The book proceeds to explore the impact of continuous, unsharp measurement on a single quantum system, where the results are evaluated in the form of steady state solutions of the variance in position and momentum. The asymptotic solutions show that continuous measurement and feedback can be used as a tool to create artificial potentials or nullify existing potentials.