Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 8Citation - Scopus: 7Time-Evolution of Squeezed Coherent States of a Generalized Quantum Parametric Oscillator(American Institute of Physics, 2019) Atılgan Büyükaşık, Şirin; Atılgan Büyükaşık, Şirin; Çayiç, Zehra; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyTime evolution of squeezed coherent states for a quantum parametric oscillator with the most general self-adjoint quadratic Hamiltonian is found explicitly. For this, we use the unitary displacement and squeeze operators in coordinate representation and the evolution operator obtained by the Wei-Norman Lie algebraic approach. Then, we analyze squeezing properties of the wave packets according to the complex parameter of the squeeze operator and the time-variable parameters of the Hamiltonian. As an application, we construct all exactly solvable generalized quantum oscillator models classically corresponding to a driven simple harmonic oscillator. For each model, defined according to the frequency modification in position space, we describe explicitly the squeezing and displacement properties of the wave packets. This allows us to see the exact influence of all parameters and make a basic comparison between the different models.Conference Object Dynamics of Squeezed States of a Generalized Quantum Parametric Oscillator(IOP Publishing, 2019) Atılgan Büyükaşık, Şirin; Çayiç, Zehra; Atılgan Büyükaşık, Şirin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyTime-evolution of squeezed coherent states of a generalized Caldirola-Kanai type quantum parametric oscillator is found explicitly using the exact evolution operator obtained by the Wei-Norman algebraic approach. Properties of these states are investigated according to the parameters of the unitary squeeze operator and the time-variable parameters of the generalized quadratic Hamiltonian. As an application, we consider exactly solvable quantum models with specific frequency modification for which the corresponding classical oscillator is in underdamping case and driving forces are of sinusoidal type. For each model we explicitly provide the evolution of the squeezed coherent states and discuss their behavior.