Repository: Freie Universität Berlin, Math Department

Quantum dynamics of a plane pendulum

Leibscher, M. and Schmidt, B. (2009) Quantum dynamics of a plane pendulum. Phys. Rev. A, 80 (1). 012510.

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A semi-analytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schrödinger equation is solved for pendular analogues of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time-evolution of the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed.

Item Type:Article
Subjects:Physical Sciences > Physics > Mathematical & Theoretical Physics > Quantum Mechanics
Physical Sciences > Physics > Chemical Physics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:449
Deposited By: BioComp Admin
Deposited On:02 Apr 2009 08:28
Last Modified:03 Mar 2017 14:40

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