solution of the time-dependent couped oscillators and coherent states for the inverted oscillator

Abstract

In this thesis, we presented the definition of the invariant theory in quantum mechanics that allows us to treat the problems of time-dependent systems and find the solution of the Schrödinger equation. Then, we studied the time-dependent coupled oscillator of a two dimensional (2D), pointing out the errors made by the method of Hassoul et al. Next, we introduced the concepts of PT-symmetry, the pseudo-hermiticity and CPT. Finally, we have constructed the coherent states for the inverted oscillator that minimize the quantum mechanical uncertainty between the position and the momentum.