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Pointwise and generalized virial theorems
Author(s) -
Levy Mel
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560140827
Subject(s) - pointwise , virial theorem , eigenvalues and eigenvectors , mathematics , hamiltonian (control theory) , energy operator , mathematical physics , generalization , pointwise convergence , homogeneity (statistics) , operator (biology) , virial coefficient , mathematical analysis , physics , quantum mechanics , energy (signal processing) , chemistry , mathematical optimization , approx , statistics , biochemistry , repressor , galaxy , computer science , transcription factor , gene , operating system
Given an eigenstate of a time‐independent Hamiltonian, an equation is derived which generates the corresponding energy by means of a pointwise application of only the kinetic operator. Satisfaction of the equation at all points in configuration space, for arbitrary values of a scale factor, constitutes a necessary eigenstate condition. Explicit knowledge of the potential operator, other than knowledge of its homogeneity, is not required. In addition, integration of the pointwise equation yields a generalization of the familiar virial theorem.
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