A N F Aleixo and A B Balantekin 2005 J. Phys. A: Math. Gen. 38 8603 doi:10.1088/0305-4470/38/40/009
Quantum dynamics of a two-level system coupled to a shape-invariant potential
A N F Aleixo1 and A B Balantekin2
Show affiliationsThe quantum dynamics of a two-level system coupled to a shape-invariant potential is investigated. Shape-invariant potentials share an integrability condition called shape invariance which identifies an underlying algebraic structure, in general infinite dimensional, that transforms the potential parameters such as strength, range and diffuseness. We determine the time-evolution operator, the density operator of the system, and obtain the temporal behaviour of various dynamical variables by considering either pure or mixed initial states of the system, constructed with the generalized coherent state of the shape-invariant coupling potential. We consider specific examples of shape-invariant coupling potentials (harmonic oscillator, Pöschl–Teller and self-similar potentials). The results obtained for all dynamical variables exhibit rapid oscillations which periodically collapse and regenerate in different ways depending on the coupling potential nature.
- PACS
- MSC
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81R15 Operator algebra methods (See also 46Lxx, 81T05)
81Q60 Supersymmetric quantum mechanics
81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
- Subjects
- Dates
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Issue 40 (7 October 2005)
Received 8 May 2005, in final form 30 August 2005
Published 21 September 2005
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Quantum dynamics of a two-level system coupled to a shape-invariant potential
A N F Aleixo and A B Balantekin 2005 J. Phys. A: Math. Gen. 38 8603
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