General formulation of rovibrational kinetic energy operators and matrix elements in internal bond-angle coordinates using factorized Jacobians

2016 ◽  
Vol 145 (23) ◽  
pp. 234102 ◽  
Author(s):  
Wassja A. Kopp ◽  
Kai Leonhard
Keyword(s):  
Kinetic Energy ◽  
Internal Bond ◽  
Bond Angle ◽  
Matrix Elements

Kinetic Energy Matrix Elements for Linear Molecules

1951 ◽  
Vol 19 (7) ◽  
pp. 982-983 ◽  
Author(s):  
Salvador M. Ferigle ◽  
Arnold G. Meister
Keyword(s):  
Kinetic Energy ◽  
Matrix Elements ◽  
Energy Matrix ◽  
Linear Molecules

scholarly journals A theory of electrons and protons

1930 ◽  
Vol 126 (801) ◽  
pp. 360-365 ◽  
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Kinetic Energy ◽  
Matrix Representation ◽  
Stationary States ◽  
Matrix Elements ◽  
The Matrix ◽  
Spin Properties

The relativity quantum theory of an electron moving in a given electro­magnetic field, although successful in predicting the spin properties of the electron, yet involves one serious difficulty which shows that some fundamental alteration is necessary before we can regard it as an accurate description of nature. This difficulty is connected with the fact that the wave equation, which is of the form [W/ c + e / c A 0 + ρ 1 (σ, p + e / c A) + ρ 3 mc ] Ψ = 0, (1) has, in addition to the wanted solutions for which the kinetic energy of the electron is positive, an equal number of unwanted solutions with negative kinetic energy for the electron, which appear to have no physical meaning. Thus if we take the case of a steady electromagnetic field, equation (1) will admit of periodic solutions of the form Ψ = u e - i E t / h , (2) where u is independent of t , representing stationary states, E being the total energy of the state, including the relativity term mc 2 . There will then exist solutions (2) with negative values for E as well as those with positive values ; in fact, if we take a matrix representation of the operators ρ 1 σ 1 , ρ 1 σ 2 , ρ 1 σ 3 , ρ 3 with the matrix elements all real, then the conjugate complex of any solution of (1) will be a solution of the wave equation obtained from (1) by reversal of the sign of the potentials A, and either the original wave function or its con­jugate complex must refer to a negative E.

PHOTOELECTRON DIFFRACTION STUDY OF THE (3×3)-Sn/Ge(111) STRUCTURE

1999 ◽  
Vol 06 (06) ◽  
pp. 1091-1096 ◽  
Author(s):  
L. FLOREANO ◽  
L. PETACCIA ◽  
M. BENES ◽  
D. CVETKO ◽  
A. GOLDONI ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Diffraction Study ◽  
Energy Dependence ◽  
Storage Ring ◽  
Nearest Neighbor ◽  
Bond Angle ◽  
Emission Angle ◽  
Photon Polarization ◽  
Direction Parallel ◽  
Photoelectron Diffraction

The photoemission spectra of the Sn 4d electrons from the (3×3)-Sn/Ge(111) surface present two components which are attributed to inequivalent Sn atoms in T4 bonding sites. This structure has been explored by photoelectron diffraction experiments performed at the ALOISA beamline of the Elettra storage ring in Trieste (Italy). The modulation of the intensities of the two Sn components, caused by the backscattering of the underneath Ge atoms, has been measured as a function of the emission angle at fixed kinetic energies and vice versa. The bond angle between Sn and its nearest neighbor atoms in the first Ge layer ( Sn–Ge 1) has been measured by taking polar scans along the main symmetry directions and it was found almost equivalent for the two components. The corresponding bond lengths are also quite similar, as obtained by studying the dependence on the photoelectron kinetic energy with the photon polarization and the collection direction parallel to the Sn–Ge 1 bond orientation (bond emission). A clear difference between the two bonding sites is observed when studying the energy dependence at normal emission, where the sensitivity to the Sn height above the Ge atom in the second layer is enhanced. The (3×3)-Sn/Ge(111) is thus characterized by a structure where the Sn atom and its three nearest neighbor Ge atoms form a rather rigid unit that presents a strong vertical distortion with respect to the underneath atom of the second Ge layer.

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