AN INVESTIGATION OF MOLECULAR SPECTROSCOPY WITH GEOMETRIC ALGEBRA
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Keywords:Geometric Algebra, Operator of the kinetic energy, covariant metric tensor, Rotational measuring vectors, Vibrational measuring vectors
In this study Geometric Algebra was used to create a general and practical method for obtaining the operators of the kinetic energy of the molecular vibration-rotation of polyatomic molecules. On the other hand, these polyatomic molecules' precise intrinsic kinetic energy operators include a metric tensor. The elements of this metric tensor were expressed as the massweighted sum of measuring vector inner product vectors compatible with the molecule's nucleus. Whereas, the vibrational and rotational measuring vectors that appear in the metric tensor for any geometrically defined coordinates of the shape and frames of the body were easily determined using geometric algebra. The current method (geometric algebra) generates molecular vibration-rotation kinetic energy operators that are in perfect agreement with earlier studies. Finally, we have used the Lagrangian Formulation where the component of kinetic energy was expressed in the form of generalized velocities.Using geometric products, we discovered the relation between the covariant metric tensor and the contravariant metric tensor.
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