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Many-body Reduced Vector Solution and Water Vibrations
A.S. Abdel-Rahman

Reduced mass value and vector are well known for the two-body problem, but the many-body reduced vector problem is not solved yet. The study of many-body problems and their applications (such as vibrational spectroscopy) is one of the more important physical problems. Vibrational spectroscopy provides a powerful tool to perceive the molecular structures and atom motions of molecules. The water molecule is a three-body system stretching vibration that has been previously quantized; their frequencies were defined and showed the infrared (IR) absorption spectrum based on Morse potential. In this work, the reduced mass of the many-body problem is being solved and then used to study the intensity of the stretching vibration modes and show the ratio is in agreement with experiments. The molecule was studied in classical and quantum mechanics to determine its absorption intensity as an example of a reduced mass problem. The results show molecular atomic motions and changes in dipole and reduced mass vector. A Morse-like model for bending was predicted based on the spectroscopic vibration frequency and intensity, defining the bending potential depth of 93.5 kJ/mol.

Keywords: many-body problem; reduced mass; Morse potential; vibration; bending model; water.