scholarly journals Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization

2018 ◽  
Vol 149 (13) ◽  
pp. 134110 ◽  
Author(s):  
Niels Kristian Madsen ◽  
Mads Bøttger Hansen ◽  
Alberto Zoccante ◽  
Kasper Monrad ◽  
Mikkel Bo Hansen ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Wave Functions ◽  
Time Dependent ◽  
Second Quantization ◽  
Exponential Parameterization

Quantum dynamics of a general time-dependent coupled oscillator

2021 ◽  
pp. 2150230
Author(s):  
Sara Hassoul ◽  
Salah Menouar ◽  
Jeong Ryeol Choi ◽  
Ramazan Sever
Keyword(s):  
Quantum Dynamics ◽  
Oscillatory System ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
Coupled Oscillator ◽  
Quantum Invariant ◽  
Classical Counterpart ◽  
Quantum Dynamical ◽  
General Time

Quantum dynamical properties of a general time-dependent coupled oscillator are investigated based on the theory of two-dimensional (2D) dynamical invariants. The quantum dynamical invariant of the system satisfies the Liouville–von Neumann equation and it coincides with its classical counterpart. The mathematical formula of this invariant involves a cross term which couples the two oscillators mutually. However, we show that, by introducing two pairs of annihilation and creation operators, it is possible to uncouple the original invariant operator so that it becomes the one that describes two independent subsystems. The eigenvalue problem of this decoupled quantum invariant can be solved by using a unitary transformation approach. Through this procedure, we eventually obtain the eigenfunctions of the invariant operator and the wave functions of the system in the Fock state. The wave functions that we have developed are necessary in studying the basic quantum characteristics of the system. In order to show the validity of our theory, we apply our consequences to the derivation of the fluctuations of canonical variables and the uncertainty products for a particular 2D oscillatory system whose masses are exponentially increasing.

scholarly journals Chaos in time-dependent variational approximations to quantum dynamics

1998 ◽  
Vol 57 (2) ◽  
pp. 1489-1498 ◽  
Author(s):  
Fred Cooper ◽  
John Dawson ◽  
Salman Habib ◽  
Robert D. Ryne
Keyword(s):  
Quantum Dynamics ◽  
Time Dependent ◽  
Variational Approximations

scholarly journals Reciprocity between moduli and phases in time-dependent wave functions

1999 ◽  
Vol 60 (3) ◽  
pp. 1802-1810 ◽  
Author(s):  
R. Englman ◽  
A. Yahalom
Keyword(s):  
Wave Functions ◽  
Time Dependent
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