# Identities, perturbative expansions, and recursion relations for mapping operators, effective Hamiltonians, and effective operators

## Related Articles

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A nonperturbative theory of predissociation based upon an effective Hamiltonian is presented. For a model diatomic system in which a (bound-state) Morse potential-energy curve is crossed by an (unbound-state) exponential potential-energy curve, the exact effective Hamiltonian may be obtained in...

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A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient...

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We consider the massless Derezinskiâ€“GÃ©rard model introduced by Derezinski and GÃ©rard in 1999. We give a sufficient condition for the existence of a ground state of the massless Derezinskiâ€“GÃ©rard model without the assumption that the Hamiltonian of particles has compact...

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In the Hamiltonian formulation, classical mechanics employs the commutative algebra of functions that are defined on phase space a point of which could be represented using Dirac delta distributions. In the absence of such a concrete existence of the notion of point in the quantum domain, we...

- Averaging principle for a class of stochastic reactionï¿½diffusion equations. Cerrai, Sandra; Freidlin, Mark // Probability Theory & Related Fields;May2009, Vol. 144 Issue 1/2, p137
We consider the averaging principle for stochastic reactionï¿½diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in...

- Diagrammatic complete active space perturbation theory. Finley, James P. // Journal of Chemical Physics;1/15/1998, Vol. 108 Issue 3, p1081
Formulates a diagrammatic complete active space second-order perturbation theory. Basis of the theory formulation; Importance of wave operators in all Hilbert space methods; Limitation of the multireference perturbation theory; Computation of the final energy in the same manner as with state...

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We consider a two-dimensional periodic Schrï¿½dinger operator perturbed by the interaction potential of two one-dimensional particles. We prove that quasilevels (i.e., eigenvalues or resonances ) of the given operator exist for a fixed quasimomentum and a small perturbation near the band...

- Perturbative approaches to highly excited molecular vibrations of H2O, D2O, and HDO. McCoy, Anne B.; Silbert, Edwin L. // Journal of Chemical Physics;2/1/1990, Vol. 92 Issue 3, p1893
Molecular vibrations of water are studied using Van Vleck perturbation theory. In these calculations, the OH stretches are expressed in terms of the Morse coordinate, yi =[1-exp(-Î±ri)]/Î±, and its conjugate momentum, while the bend is treated in a traditional manner. Nearly degenerate...

- Effects of symmetry-breaking perturbations on excitonic states bound to systems of reduced symmetry. Francoeur, S.; Marcet, S. // Journal of Applied Physics;Sep2010, Vol. 108 Issue 4, p043710
Using an invariant expansion, we build an Hamiltonian describing the influence of the crystal-field, the electron-hole exchange interaction, and any symmetry-breaking perturbations on the fine structure of excitons bound to systems of reduced symmetry: D2d, C3v, and C2v. Several perturbations...