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Manuscript Title: LUCY: a Fortran implementation of semiclassical spectral quantization.
Authors: M.A. Mehta, N. De Leon
Program title: LUCY
Catalogue identifier: ABDO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)115
Programming language: Fortran.
Computer: MICROVAX II.
Operating system: VAX VMS, VERSION 4.5.
Word size: 32
Keywords: Molecular, Vibration, Semiclassical spectral Quantization, Arbitrary trajectory, Phase coherence, Linear extrapolation, Ebk quantization.
Classification: 16.3.

Nature of problem:
The calculation of several semiclassical energies and eigenfunctions of the bound states of a vibrational Hamiltonian using an arbitrary (non- quantizing) trajectory.

Solution method:
Given a set of inital conditions in a quasiperiodic region of phase space, a trajectory is numerically generated. The semiclassical wave- functions are obtained by allowing the associated de Broglie wave to constructively interfere with itself at one of the spectral frequencies. The frequencies are taken from the power spectrum of the autocorrelation function of the SC wavefunction from time t=0 to time t=T. The semi- classical energies are calculated using the semiclassical eigen- functions. Starting trajectories from a point of equipotential introduces time reversal symmetry which can be taken advantage of to reduce the computation time.

Restrictions:
The potential may have only polynomials in the coordinates upto sixth power. Higher powers are possible with a slight modification to the program. It is possible to obtain the energies and eigenfunctions of multiple quantum states for a Hamiltonian with several (up to six or more) degrees of freedom. As the number of degrees of freedom increase, the measure of the energetically available phase space increases. This necessitates the propagation of the trajectory for relatively long times to allow it to sample a representative amount of phase space. One must also be careful not to venture too close to the chaotic regions as it becomes difficult to quantize in these regions.

Unusual features:
LUCY does not require the user to supply any subroutines, only a description of the Hamiltonian. Once the Hamiltonian is described, LUCY generates all functions specific to the Hamiltonian. Time reversal symmetries are automatically handled. At the lowest level LUCY can be used as a simple integrator to integrate the equations of motion and determine the fundamental frequencies of the various degrees of freedom.