Invariantes dinâmicos, estados coerentes e fases geométricas em mecânica quântica - Lima, Dibartolomei Antônio Pereira de (2014)
In this thesis, we study the generalized harmonic oscillator with frequency dependent mass and time and subjected to a friction force whose speed depends on the time, of classical and quantum points of view. Obtained the solutions of the classical equation of motion of this system for some special cases, we derive an equation of motion that describes three systems. Then, with the help of quadratic invariant operators the light of the method of dynamical invariants we find the exact solutions of the Schrodinger equation for this system. We derive the geometric, dynamic and Berry for this system non-stationary phases and we evaluate this phases for three special cases. After this, we construct coherent states for this quantized system and employ them to investigate some properties quantum properties such as quantum uctuations of the coordinate and momentum as well as the product of the uncertainties. We then use a linear invariant operator light of the method of dynamical invariants in the intention of finding exact Schrodinger equation for the damped harmonic oscillator for forced time-dependent solutions. As described in our contribution we built solutions in the form of Gaussian wave packets as well as calculate the quantum uctuations of the coordinates and time, as well as the correlations between them. Finally, we show that the width of the uctuations and correlations of the Gaussian packet does not depend on the external force