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Author Mandal, Anirban ♦ Hunt, Katharine L. C.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ ATOMIC AND MOLECULAR PHYSICS ♦ CHARGED PARTICLES ♦ COORDINATES ♦ ELECTROMAGNETIC FIELDS ♦ EXPECTATION VALUE ♦ GAUGE INVARIANCE ♦ HAMILTONIANS ♦ LAGRANGIAN FUNCTION ♦ MOLECULES ♦ POTENTIALS ♦ QUANTUM MECHANICS ♦ SCALARS ♦ TIME DEPENDENCE ♦ VECTORS
Abstract In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term H{sub m} and a field term H{sub f}, and show that both H{sub m} and H{sub f} have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2016-01-28
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 144
Issue Number 4


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