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Harmonic Oscillator
Heisenberg Algebra
Quantum Physics
Second Order Equation
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A symmetry trip from Caldirola to Bateman damped systems
A symmetry trip from Caldirola to Bateman damped systems,V. Aldaya,F. Coss' Dio,J. Guerrero,F. F. LópezRuiz
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A symmetry trip from Caldirola to Bateman damped systems
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V. Aldaya
,
F. Coss' Dio
,
J. Guerrero
,
F. F. LópezRuiz
For the CaldirolaKanai system, describing a quantum damped harmonic oscillator, a couple of constantofmotion operators generating the
Heisenberg algebra
can be found. The inclusion of the standard time evolution symmetry in this algebra for damped systems, in a unitary manner, requires a nontrivial extension of this basic algebra and hence the physical system itself. Surprisingly, this extension leads directly to the socalled Bateman's dual system, which now includes a new particle acting as an energy reservoir. The group of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a firstorder Schr\"odinger equation. The usual secondorder equation and the inclusion of the original CaldirolaKanai model in Bateman's system are also discussed.
Published in 2011.
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References
(3)
Quantum Optics
(
Citations: 2976
)
D. G. C. Jones
Journal:
Nature
, vol. 245, no. 5426, pp. 430430, 1973
Geometrical methods in the theory of ordinary differential equations
(
Citations: 837
)
V. I. Arnold
Published in 1988.
Discrete basis of localized quantum states for the free particle
(
Citations: 1
)
Julio Guerrero
,
Francisco F. LopezRuiz
,
Victor Aldaya
,
Francisco Cossio
Published in 2010.
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Citations
(1)
The quantum Arnold transformation
(
Citations: 1
)
Victor Aldaya
,
Francisco Cossio
,
Julio Guerrero
,
Francisco F. LopezRuiz
Published in 2010.