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i-manager s Journal on Material Science

Revival And Collapse Of The Vibrational State Wave Packet For Diatomic Molecule In An Anharmonic Potential

Published Jan 1, 2015• 0 citations
Publisher

Abstract

This paper presents the time evolution of a quantum wave packet bound in the Morse potential. The quantum wave packet is the superposition of vibrational energy levels of a diatomic molecule in an anharmonic potential. The probability density function, auto-correlation function, and various time scales have been used to explore the revival pattern of this wave packet. The dynamics of the wave packet with respect to time shows a series of collapses and the subsequent revivals. The results are presented for CO molecule.

DOI
10.26634/jms.3.1.3369

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This paper presents the time evolution of a quantum wave packet bound in the Morse potential. The quantum wave packet is the superposition of vibrational energy levels of a diatomic molecule in an anharmonic potential. The probability density function, auto-correlation function, and various time scales have been used to explore the revival pattern of this wave packet. The dynamics of the wave packet with respect to time shows a series of collapses and the subsequent revivals. The results are presented for CO molecule.
We investigate the dynamics of a rotating Morse wave packet, appropriate for a ro-vibrating diatomic molecule. The coupling between vibrational and rotational degrees of freedom is explicated in real position space as well as in phase space Wigner distribution of a SU(2) coherent state at various dynamically evolved times. We choose the well studied I2I_{2}I2​ molecule with the parameter values in good agrement with experiments. A quantitative measure of the angles of rotations for different angular momenta is also given.
The general properties of the time-dependent characteristics of one-dimensional vibrational wave packets in an anharmonic system with the quadratic spectrum are discussed. The local behavior of the autocorrelation function and its square modulus (the survival function) is studied near the moments of fractional revival t=(p/q)Trev, where Trev is the period of the complete revival, p/q is an irreducible fraction, and q is the order of the revival. It is shown that all the wave packets have the same values of the survival function at the moments of fractional revival provided that the number of states in the packet exceeds the order of the revival q. It is also found that for the given packet, all the fractional revivals are identical to each other in the sense that their lifetimes do not depend on the order of the revival. The lifetimes of all fractional revivals are expressed in terms of the parameters of the initial packet (the effective number of states and the period of classical motion of the packet center) and the anharmonicity of the molecular system.
We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopic-quantum-superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.
Abstract The time evolution of wave packets in the Morse potential is investigated under the influence of the environment consisting of harmonic oscillators. We obtain a Markovian master equation that incorporates the fact that due to the nonequidistant spectrum, the relaxation rate of each energy eigenstate is different. The nonunitary time evolution is visualized by the aid of the Wigner function related to the reduced density operator of the Morse system. The time scale of decoherence is much shorter than that of dissipation, and gives rise to states which are mixtures of localized states along the phase space orbit of the corresponding classical particle. This behaviour is to a large extent independent of the coupling strength, the temperature of the environment and also of the initial state.
The behavior of Hydrogen Rydberg wave packets on time scales much greater than trev was studied.After a few revival cycles the wave packet ceases to reform at multiples of the revival time.Instead,a new series of collapses and revivals commences.Its periodicity is tsr(tsrtrev).The wave packet that forms at time tsr more closely resembles the initial packet than does the full revival packet at time trev.An explanation of these effects is given by constructing autocorrelation function and using the relationship between the wave function and those subsidiary wave functions.
We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.