The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Alain Joye - One of the best experts on this subject based on the ideXlab platform.
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A Time-Dependent Born-Oppenheimer Approximation with Exponentially Small Error Estimates
Communications in Mathematical Physics, 2001Co-Authors: George A. Hagedorn, Alain JoyeAbstract:We present the construction of an exponentially accurate time-dependent Born–Oppenheimer Approximation for molecular quantum mechanics.
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a time dependent born Oppenheimer Approximation with exponentially small error estimates
arXiv: Mathematical Physics, 2000Co-Authors: George A. Hagedorn, Alain JoyeAbstract:We present the construction of an exponentially accurate time-dependent Born-Oppenheimer Approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to $\epsilon^{-4}$, where $\epsilon$ is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time-dependent Schr\"odinger equation that agree with exact normalized solutions up to errors whose norms are bounded by $\ds C \exp(-\gamma/\epsilon^2)$, for some C and $\gamma>0$.
George A. Hagedorn - One of the best experts on this subject based on the ideXlab platform.
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Diatomic molecules with large angular momentum in the Born–Oppenheimer Approximation
Journal of Physics A: Mathematical and Theoretical, 2008Co-Authors: Sharon M Hughes, George A. HagedornAbstract:The standard Born–Oppenheimer Approximation for a diatomic molecule yields an expansion in powers of for the bound state associated with a given electron energy level, a fixed vibrational quantum number n and a fixed nuclear angular momentum quantum number l. The expansion parameter is the fourth root of the ratio of the electron mass divided by the mean nuclear mass. In this paper, we present an explicit Approximation whose errors are uniformly bounded by C5 whenever the nuclear angular momentum quantum number satisfies l < κ−3/2. We apply our Approximation to the H+2 and HD+ ions and compare the results with published rotational–vibrational energies.
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The AC Stark Effect, Time-Dependent Born–Oppenheimer Approximation, and Franck–Condon Factors
Annales Henri Poincaré, 2006Co-Authors: George A. Hagedorn, Vidian Rousse, Steven W. JilcottAbstract:We study the quantum mechanics of a simple molecular system that is subject to a laser pulse. We model the laser pulse by a classical oscillatory electric field, and we employ the Born–Oppenheimer Approximation for the molecule. We compute transition amplitudes to leading order in the laser strength. These amplitudes contain Franck–Condon factors that we compute explicitly to leading order in the Born–Oppenheimer parameter. We also correct an erroneous calculation in the mathematical literature on the AC Stark effect for molecular systems. Communicated by Christian Gérard.
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The AC Stark Effect, Time-Dependent Born–Oppenheimer Approximation, and Franck–Condon Factors
Annales Henri Poincaré, 2006Co-Authors: George A. Hagedorn, Vidian Rousse, Steven W. JilcottAbstract:We study the quantum mechanics of a simple molecular system that is subject to a laser pulse. We model the laser pulse by a classical oscillatory electric field, and we employ the Born–Oppenheimer Approximation for the molecule. We compute transition amplitudes to leading order in the laser strength. These amplitudes contain Franck–Condon factors that we compute explicitly to leading order in the Born–Oppenheimer parameter.
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A Time-Dependent Born-Oppenheimer Approximation with Exponentially Small Error Estimates
Communications in Mathematical Physics, 2001Co-Authors: George A. Hagedorn, Alain JoyeAbstract:We present the construction of an exponentially accurate time-dependent Born–Oppenheimer Approximation for molecular quantum mechanics.
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a time dependent born Oppenheimer Approximation with exponentially small error estimates
arXiv: Mathematical Physics, 2000Co-Authors: George A. Hagedorn, Alain JoyeAbstract:We present the construction of an exponentially accurate time-dependent Born-Oppenheimer Approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to $\epsilon^{-4}$, where $\epsilon$ is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time-dependent Schr\"odinger equation that agree with exact normalized solutions up to errors whose norms are bounded by $\ds C \exp(-\gamma/\epsilon^2)$, for some C and $\gamma>0$.
Boris Zhilinskii - One of the best experts on this subject based on the ideXlab platform.
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topological properties of the born Oppenheimer Approximation and implications for the exact spectrum
Letters in Mathematical Physics, 2001Co-Authors: Frédéric Faure, Boris ZhilinskiiAbstract:The Born–Oppenheimer Approximation can generally be applied when a quantum system is coupled with another comparatively slower system which is treated classically: for a fixed classical state, one considers a stationary quantum vector of the quantum system. Geometrically, this gives a vector bundle over the classical phase space of the slow motion. The topology of this bundle is characterized by integral Chern classes. In the case where the whole system is isolated with a discrete energy spectrum, we show that these integers have a direct manifestation in the qualitative structure of this spectrum: the spectrum is formed by groups of levels and these integers determine the precise number of levels in each group.
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Topological Properties of the Born–Oppenheimer Approximation and Implications for the Exact Spectrum
Letters in Mathematical Physics, 2001Co-Authors: Frédéric Faure, Boris ZhilinskiiAbstract:The Born–Oppenheimer Approximation can generally be applied when a quantum system is coupled with another comparatively slower system which is treated classically: for a fixed classical state, one considers a stationary quantum vector of the quantum system. Geometrically, this gives a vector bundle over the classical phase space of the slow motion. The topology of this bundle is characterized by integral Chern classes. In the case where the whole system is isolated with a discrete energy spectrum, we show that these integers have a direct manifestation in the qualitative structure of this spectrum: the spectrum is formed by groups of levels and these integers determine the precise number of levels in each group.
Stefan Teufel - One of the best experts on this subject based on the ideXlab platform.
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The time-dependent Born-Oppenheimer Approximation
Mathematical Modelling and Numerical Analysis, 2007Co-Authors: Gianluca Panati, Herbert Spohn, Stefan TeufelAbstract:We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer Approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer Approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.
Brian T. Sutcliffe - One of the best experts on this subject based on the ideXlab platform.
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An analysis of the role of the Born--Oppenheimer Approximation in calculating rotational--vibrational interactions in molecules
Theoretical Chemistry Accounts, 2011Co-Authors: Brian T. SutcliffeAbstract:It is argued that whether the use of the Born--Oppenheimer Approximation is thought to require consideration of the potential energy surface in the context of a full Coulomb Schrödinger Hamiltonian in which translational and rotational motions are explicitly considered, and then it is inconsistent to treat that surface without allowing for the rotational motion of the molecule. Some of the implications of this upon the calculation of partition functions are considered.
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Chemistry as a “Manifestation of Quantum Phenomena” and the Born–Oppenheimer Approximation?
Structure and Bonding, 2011Co-Authors: Brian T. SutcliffeAbstract:When considering the work of Carl Ballhausen on vibrational spectra, it is suggested that his use of the Born–Oppenheimer Approximation is capable of some refinement and extension in the light of later developments. A consideration of the potential energy surface in the context of a full Coulomb Schrodinger Hamiltonian in which translational and rotational motions are explicitly considered would seem to require a reformulation of the Born–Oppenheimer approach. The resulting potential surface for vibrational motion should be treated, allowing for the rotational motion and the nuclear permutational symmetry of the molecule.