Quantum dynamics of a plane pendulum

摘要: 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 Schrodinger equation solved for pendular analogues coherent and squeezed states harmonic oscillator, induced by instantaneous changes periodic potential energy function. Coherent are discussed between limit small displacements inverted limit, while shown interpolate vibrational free rotational motion. In latter case, full fractional revivals well spatiotemporal structures in time-evolution probability densities (quantum carpets) quantitatively analyzed. Corresponding expressions mean orientation derived terms time. For double potentials, different revival schemes carpets found even odd initial forming ground tunneling doublet. Time evolution alignment allows separation with parity. Implications external (rotational) internal (torsional) motion molecules intense laser fields discussed.