Quantum dynamics of a plane pendulum

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.012510· OSTI ID:21313252

Leibscher, Monika ^[1]; Schmidt, Burkhard ^[2]

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1. Institut fuer Chemie und Biochemie, Freie Universitaet Berlin, Takustr. 3, D-14195 Berlin (Germany)
2. Institut fuer Mathematik, Freie Universitaet Berlin, Arnimallee 6, D-14195 Berlin (Germany)

A semianalytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schroedinger equation is solved for pendular analogs 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.

• OSTI ID: 21313252
• Journal Information: Physical Review. A, Vol. 80, Issue 1; Other Information: DOI: 10.1103/PhysRevA.80.012510; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALIGNMENT
DENSITY
EVOLUTION
HARMONIC OSCILLATORS
LASER RADIATION
MOLECULES
ORIENTATION
PARITY
PERIODICITY
PHOTON-MOLECULE COLLISIONS
POTENTIAL ENERGY
POTENTIALS
PROBABILITY
ROTATIONAL STATES
SCHROEDINGER EQUATION
TIME DEPENDENCE
TUNNEL EFFECT
VIBRATIONAL STATES
WAVE FUNCTIONS