Symmetry Properties of the Kinetic Energy Matrix and Their Applications to Problems of Molecular Vibrations

1970 ◽  
Vol 53 (9) ◽  
pp. 3450-3452 ◽  
Author(s):  
Giovanna Dellepiane ◽  
Mariangela Gussoni ◽  
Giuseppe Zerbi
Keyword(s):  
Kinetic Energy ◽  
Molecular Vibrations ◽  
Energy Matrix ◽  
Symmetry Properties

Intervalley kinetic energy terms in the effective mass equation: a one-dimensional analytical study

1989 ◽  
Vol 67 (9) ◽  
pp. 896-903 ◽  
Author(s):  
Lorenzo Resca
Keyword(s):  
Kinetic Energy ◽  
Effective Mass ◽  
Analytical Study ◽  
Three Dimensional ◽  
Real Space ◽  
The Other ◽  
Alternative Formulation ◽  
One Dimensional ◽  
Symmetry Properties ◽  
Band Case

We show that a one-dimensional analytical study allows us to test and clarify the derivation, assumptions, and symmetry properties of the intervalley effective mass equation (IVEME). In particular, we show that the IVEME is consistent with a two-band case, and is in fact exact for a model that satisfies exactly all its assumptions. On the other hand, an alternative formulation in k-space that includes intervalley kinetic energy terms is consistent with a one-band case, provided that intra-valley kinetic energy terms are also calculated consistent with one band. We also show that the standard symmetry assumptions for both real space and k-space formulations are not actually exact, but are consistent with a "total symmetric" projection, or with taking spherical averages in a three-dimensional case.

Natural Frequencies of a Body of Revolution Vibrating Transversely in a Fluid

1971 ◽  
Vol 15 (02) ◽  
pp. 97-114
Author(s):  
Louis Landweber
Keyword(s):  
Kinetic Energy ◽  
Circular Cylinder ◽  
Final Section ◽  
Natural Frequencies ◽  
The Body ◽  
Body Of Revolution ◽  
Energy Matrix ◽  
Potential Energy Matrix ◽  
Strip Theory

IN A PREVIOUS PAPER [1]3 a procedure for determining the natural frequencies of a body vibrating in a fluid was described and applied to a flexible circular cylinder. A more practical and more difficult application of the method, to the case of a body of revolution, is presented in the present work. As was shown in [1], the natural frequencies are given by the eigenvalues of the potential energy matrix of the elastic body with respect to an inertia matrix, the latter being derived from the mass distribution of the body and the kinetic energy of the fluid. Thus two matrices must be obtained, and since the determination of the former is a problem in elasticity, and the determination of the latter one in hydrodynamics, these will be treated in separate sections. Then, in the final section, a particular body of revolution with prescribed elastic and inertial characteristics will be assumed, and its natural frequencies of vibration in air and in water will be calculated. For vibration in water, results obtained by means of strip theory and by the present matrix technique will be compared.

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

Ratios of Isotopic Frequencies Using HLFS Method

1978 ◽  
Vol 33 (12) ◽  
pp. 1590-1591
Author(s):  
T. R. Ananthakrishnan
Keyword(s):  
Kinetic Energy ◽  
Small Molecules ◽  
Low Frequency ◽  
Separation Method ◽  
Frequency Separation ◽  
Product Rule ◽  
Energy Matrix

Abstract Simple expressions involving elements of the kinetic energy matrix are obtained for the ratios of isotopic frequencies in the case of vibrational species, of order two and three, associated with small molecules by employing the high and low frequency separation method and the product rule. The applicability of the method is indicated.

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