Virial Theorem for a Molecule Page: III
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TABLE OF CONTENTS
Page
I. INTRODUCTION 1
II. VIRIAL THEOREM IN CLASSICAL MECHANICS .... 5
III. VIRIAL THEOREM IN QUANTUM MECHANICS
FOR EXACT WAVE FUNCTION 9
IV. VIRIAL THEOREM FROM A TRIAL WAVE
FUNCTION 12
Simple Scaling 13
For the Whole Molecule 13
Simple scaling for the Case
of Fixed Nuclei 15
Generalized Scaling for the
Whole Molecule 17
V. BORN-OPPENHEIMER APPROXIMATION 21
Transformation to Body
Fixed Coordinates 22
Transformation 22
Transformation of the Hamiltonian .... 23
Separation of the Center of Mass Motion . . 26
Separation of the Electronic and Nuclear
Motion 27
VI. VIRIAL THEOREM IN BORN-OPPENHEIMER
APPROXIMATION FROM AN EXACT WAVE
FUNCTION 30
Electronic Equation . 30
Nuclear Equation 31
Relation Between the Virial Theorem in
the Born-Oppenheimer Approximation and
the Exact Virial Theorem for the Whole
Molecule 32
in
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Ranade, Manjula A. Virial Theorem for a Molecule, thesis, May 1972; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc131519/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .