Time 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.
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June 2019
Research Article|
June 14 2019
Time-evolution of squeezed coherent states of a generalized quantum parametric oscillator
Şirin A. Büyükaşık;
Şirin A. Büyükaşık
Department of Mathematics, Izmir Institute of Technology
, 35430 Urla, Izmir, Turkey
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Zehra Çayiç
Zehra Çayiç
Department of Mathematics, Izmir Institute of Technology
, 35430 Urla, Izmir, Turkey
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J. Math. Phys. 60, 062104 (2019)
Article history
Received:
July 31 2018
Accepted:
May 19 2019
Citation
Şirin A. Büyükaşık, Zehra Çayiç; Time-evolution of squeezed coherent states of a generalized quantum parametric oscillator. J. Math. Phys. 1 June 2019; 60 (6): 062104. https://doi.org/10.1063/1.5050489
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