Nonrelativistic Hamiltonian

An Extended (Sufficiency) Criterion for the Vanishing of the Tensorial Field Observability of Molecular States in a Hamiltonian Formalism An Interpretation Lagrangeans in Phase-Modulus Formalism A. Background to the Nonrelativistic and Relativistic Cases Nonreladvistic Electron... 

We find it convenient to reverse the historical ordering and to stait with (neatly) exact nonrelativistic vibration-rotation Hamiltonians for triatomic molecules. From the point of view of molecular spectroscopy, the optimal Hamiltonian is that which maximally decouples from each other vibrational and rotational motions (as well different vibrational modes from one another). It is obtained by employing a molecule-bound frame that takes over the rotations of the complete molecule as much as possible. Ideally, the only remaining motion observable in this system would be displacements of the nuclei with respect to one another, that is, molecular vibrations. It is well known, however, that such a program can be realized only approximately by introducing the Eckart conditions [38]. 

An alternative form of exact nonrelativistic vibration-rotation Hamiltonian for triatomic molecules (ABC) is that used by Handy, Carter (HC), and... 

The nonrelativistic electronic Hamiltonian for N electrons in the field of M point charges (nuclei) under the Bom-Oppenheimer approximation is given by... 

Therefore in the presence of an external electric field of strength Ez in the -direction, the total nonrelativistic molecular Hamiltonian is... 

The relativistic treatment of electron EDM begins by replacing the nonrelativistic Hamiltonian H and the interaction Hamiltonian Hi by their relativistic counterparts... 

The nonrelativistic, electronic Schrodinger Hamiltonian operator, designated as H, is represented by... 

The problem of nonrelativistic limit description for fundamental particles and their interactions may be solved in different ways. Although in all methods of nonrelativistic expansion the first terms of the Hamiltonians coincide, however the difference begins to arise at transition to the higher orders of expansion. The method of Foldy-Wouthuysen... 

We would like to point out some steps of derivation of the nonrelativistic limit Hamiltonians by means of the Foldy-Wouthuyisen transformation (Bjorken and Drell, 1964). The method is based on the transformation of a relativistic equation of motion to the Schrodinger equation form. 

The time-independent nonrelativistic electronic Hamiltonian, under the Bom-Oppenheimer approximation can be written as [ 1 ]... 

The slow convergence of the doubles contributions to the AE is a general problem related to the accurate description of electron pairs in any electronic system. This problem has been studied carefully for the simplest two-electron system, namely the ground-state He atom. In nonrelativistic theory, its Hamiltonian reads... 

The valence correlation component of TAE is the only one that can rival the SCF component in importance. As is well known by now (and is a logical consequence of the structure of the exact nonrelativistic Bom-Oppenheimer Hamiltonian on one hand, and the use of a Hartree-Fock reference wavefunction on the other hand), molecular correlation energies tend to be dominated by double excitations and disconnected products thereof. Single excitation energies become important only in systems with appreciable nondynamical correlation. Nonetheless, since the number of single-excitation amplitudes is so small compared to the double-excitation amplitudes, there is no point in treating them separately. 

We consider systems consisting of two electrons and an infinitely massive nucleus of charge Z, moving subject to the nonrelativistic Hamiltonian (in hartree atomic units, me = it = c = 47r o= 1)... 

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