Journal ArticleDOI
Quantum vibrational transition probabilities from real classical trajectories: Collinear atom–diatom collisions
TLDR
In this article, the authors explore the range of validity of several such correspondence methods for collinear atom-diatom collisions by comparing the results with those from rigorous quantum mechanical calculations.Abstract:
Quantum vibrational transition probabilities may be estimated from single, real classical trajectories by exploiting the approximate correspondence between the classical and quantal motions. In this paper we explore the range of validity of several such correspondence methods for collinear atom–diatom collisions by comparing the results with those from rigorous quantum mechanical calculations. The model systems considered here include: (a) a harmonic oscillator with (1) a repulsive exponential, (2) a Landau–Teller, and (3) a Lennard‐Jones interaction potential, and (b) a Morse oscillator with a repulsive exponential interaction potential. The range of the dimensionless mass parameter M is 0.00628 to 3.737 and the total system energy ranges from 1.55 to 10.0 in units of h/ωe. For both Morse and harmonic oscillator excitation the semiclassical results are generally more accurate for small M and for small initial and final vibrational quantum numbers. Quantitatively, the results are consistently better for a...read more
Citations
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Journal ArticleDOI
Vibrational Energy Transfer Rates Using a Forced Harmonic Oscillator Model
TL;DR: In this article, the analysis, validation, and application of analytic, nonperturbative, semiclassical vibration-translation and vibration-vibration-translation (V-V-T) rate models are addressed.
Journal ArticleDOI
VV and VT rate coefficients in N2 by a quantum-classical model
TL;DR: In this article, a semi-classical 3-dimensional model was used to calculate the rate coefficients for H 2 H 2 collisions with respect to the long range and short range interaction potential.
Journal ArticleDOI
Vibrational relaxation and dissociation behind shock waves. Part 1 - Kinetic rate models.
TL;DR: In this article, the authors validate the analytical nonperturbative semiclassical vibration-translation and vibration-vibration-translation rate models for the atom-diatom and diatom-Diatom vibrational energy transfer molecular collisions.
Journal ArticleDOI
The semiclassical treatment of molecular roto/vibrational energy transfer
Journal ArticleDOI
Matrix elements for Morse oscillators
V. S. Vasan,R. J. Cross +1 more
TL;DR: In this paper, exact analytic expressions for the following matrix elements for a Morse oscillator were derived, where a is the Morse range parameter and γ is an arbitrary constant, where γ = 0.
References
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Journal ArticleDOI
Space-Time Approach to Non-Relativistic Quantum Mechanics
TL;DR: In this paper, the authors formulated non-relativistic quantum mechanics in a different way and showed that the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way.
Journal ArticleDOI
Time‐dependent approach to semiclassical dynamics
TL;DR: In this paper, a wave packet is decomposed into time-dependent wave packets, which spread minimally and which execute classical or nearly classical trajectories, assuming a Gaussian form for the wave packets and equations of motion for the Gaussians.
Journal ArticleDOI
On the Exponential Form of Time‐Displacement Operators in Quantum Mechanics
Philip Pechukas,John C. Light +1 more
TL;DR: In this paper, the authors derive and discuss a formula, due to Magnus, for the exponential representation of the operator solution to Schrodinger's equation when the Hamiltonian is time dependent.
Journal ArticleDOI
Exact Quantum-Mechanical Calculation of a Collinear Collision of a Particle with a Harmonic Oscillator
Don Secrest,B. Robert Johnson +1 more
TL;DR: In this article, a semi-empirical formula for computing quantum-mechanical transition probabilities for collinear collision of an atom with a diatomic molecule is given.
Journal ArticleDOI
Note on the forced and damped oscillator in quantum mechanics
TL;DR: In this paper, the wave equations for the forced, damped, and forced and damped oscillators were solved in closed form for an arbitrary forcing function; the solutions produced being in one-to-one correspondence w...
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