In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including the superposition of squeezed displaced number states with and without thermal noise. Also we have developed a new type of multidimensional squeeze operator including two different squeezing mechanisms. In the second part the dynamical models were given to show the interaction between modes in the nonlinear optical coupler.
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