Time-dependent invariants and generalized coherent states

We show that generalized coherent states follow Schrödinger dynamics in time-dependent potentials. The normalized wave-packets follow a classical evolution without spreading; in turn, the Schrödinger potential depends on the state through the classical trajectory. This feedback mechanism with continuous dynamical re-adjustment allows the packets to remain coherent indefinitely.

Download Full-text

Generalized coherent states for time-dependent and nonlinear Hamiltonian operators via complex Riccati equations

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/46/7/075304 ◽

2013 ◽

Vol 46 (7) ◽

pp. 075304 ◽

Cited By ~ 33

Author(s):

Octavio Castaños ◽

Dieter Schuch ◽

Oscar Rosas-Ortiz

Keyword(s):

Coherent States ◽

Riccati Equations ◽

Time Dependent ◽

Generalized Coherent States ◽

Hamiltonian Operators

Download Full-text

Generalized Coherent States of a Particle in a Time-Dependent Linear Potential

Chinese Physics Letters ◽

10.1088/0256-307x/26/7/070307 ◽

2009 ◽

Vol 26 (7) ◽

pp. 070307 ◽

Cited By ~ 3

Author(s):

L Krache ◽

M Maamache ◽

Y Saadi ◽

A Beniaiche

Keyword(s):

Coherent States ◽

Time Dependent ◽

Linear Potential ◽

Generalized Coherent States

Download Full-text

Dynamical Invariants for Generalized Coherent States via Complex Quantum Hydrodynamics

Dynamics ◽

10.3390/dynamics1020009 ◽

2021 ◽

Vol 1 (2) ◽

pp. 155-170

Author(s):

Moise Bonilla-Licea ◽

Dieter Schuch

Keyword(s):

Coherent States ◽

Equations Of Motion ◽

Bohmian Mechanics ◽

Equation Of Motion ◽

Time Dependent ◽

Auxiliary Equation ◽

Linear Potential ◽

Quantum Hydrodynamics ◽

Generalized Coherent States ◽

Dynamical Invariants

For time dependent Hamiltonians like the parametric oscillator with time-dependent frequency, the energy is no longer a constant of motion. Nevertheless, in 1880, Ermakov found a dynamical invariant for this system using the corresponding Newtonian equation of motion and an auxiliary equation. In this paper it is shown that the same invariant can be obtained from Bohmian mechanics using complex Hamiltonian equations of motion in position and momentum space and corresponding complex Riccati equations. It is pointed out that this invariant is equivalent to the conservation of angular momentum for the motion in the complex plane. Furthermore, the effect of a linear potential on the Ermakov invariant is analysed.

Download Full-text