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zeroth-order
The zeroth-order term gives the conventional shell model description.
      
The aim of this work is to present a perturbative expansion which differs from the usual expansions of quantum field theory in that it uses as zeroth-order approximation a non-Gaussian model.
      
The modified Hamilton-Jacobi equation for the deterministic component is then solved, and the resulting zeroth-order trajectories are computed.
      
The zeroth-order trajectories can hence be classified following this parameter, which indicates a transition between two different regimes for some value lying between 0 and 1.
      
In the classical case, the WKB approximation can only be applied when the thermodynamic potential has the Landau-Ginsberg form; the zeroth-order approximation coincides with Kramer's approximation.
      
In the multiple-scattering theory of K--deuterium interactions, the first-order correction to the zeroth-order (asymptotic) value of the K--deuterium elastic scattering amplitude is calculated, using Kohn's variational method for nuclear collisions.
      
Simplified procedures for generation of the self-consistent charge densities and bond orders from their zeroth-order counterparts in the PPP method are detailed.
      
The zeroth-order results which show substantial electron shifts and features suggesting charge imbalance in the amine and alkylboron accompanying reaction are modified by a self-consistent, linear α-upon-orbital charge adjustment method.
      
A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions.
      
A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions.
      
A proof is given that in a configuration interaction method the first-order interaction space contains at most only twice as many spin functions as the zeroth-order space.
      
The averaged coupled-pair functional (ACPF) method gives consistently the best agreement with experiment, but can become intractable, as rather large zeroth-order reference spaces can be required.
      
It can serve as a tool for analyzing the accuracy of approximate electron correlation methods and the validity of the Hartree-Fock wavefunction as the zeroth-order approximation.
      
Different forms of the zeroth-order Hamiltonian in second-order perturbation theory with a complete active space self-consistent
      
A new one-particle zeroth-order Hamiltonian is proposed for perturbation theory with a complete active space self-consistent field (CASSCF) reference function.
      
The new zeroth-order Hamiltonian has been tested on CH2, SiH2, NH2, CH3, N2, NO, and O2, for which full configuration interaction (FCI) results are available.
      
The zeroth-order Hamiltonian H0 is the sum of effective monomer Fockians and the zeroth-order wave functions are exact eigenfunctions of H0.
      
The zeroth-order wave functions of the ground (X?1A1 or 1 1A1) and B?1A1 (or 2 1A1) excited states are appropriately described by the first and second eigenvectors of the TCSCF secular equations.
      
It gives a zeroth-order description of the short-range spin correlation while insuring a proper translational symmetry with an appropriate projection of the local spin function over the entire lattice.
      
The present derivation yields a family of two-component relativistic Hamiltonians which can be used as zeroth-order approximation to the Dirac equation.
      
 

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