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

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Official URL: http://dx.doi.org/10.1103/PhysRevA.80.012510
Abstract
A semianalytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The timedependent 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 timeevolution 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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