TY - JOUR
T1 - Generalization of the continuous symmetry measure
T2 - The symmetry of vectors, matrices, operators and functions
AU - Dryzun, Chaim
AU - Avnir, David
PY - 2009
Y1 - 2009
N2 - In this paper we generalize a method for evaluating the continuous symmetry measure, which is a quantitative estimate of the degree of symmetry of a given object. The generalization makes it possible to calculate the degree of symmetry content for any mathematical entity that is part of metric spaces such as vectors, matrices, operators and functions. Furthermore, by this new approach one can calculate the symmetry-content values for any compact symmetry groups either finite or infinite. An advantage of the new methodology is the ability to investigate analytically problems of symmetry changes. Examples of symmetry evaluation calculations are provided, including mixing of ideal gases, evaluation of the symmetry content of a Hamiltonian operator, the 2pz orbital of the hydrogen atom, and more.
AB - In this paper we generalize a method for evaluating the continuous symmetry measure, which is a quantitative estimate of the degree of symmetry of a given object. The generalization makes it possible to calculate the degree of symmetry content for any mathematical entity that is part of metric spaces such as vectors, matrices, operators and functions. Furthermore, by this new approach one can calculate the symmetry-content values for any compact symmetry groups either finite or infinite. An advantage of the new methodology is the ability to investigate analytically problems of symmetry changes. Examples of symmetry evaluation calculations are provided, including mixing of ideal gases, evaluation of the symmetry content of a Hamiltonian operator, the 2pz orbital of the hydrogen atom, and more.
UR - http://www.scopus.com/inward/record.url?scp=70350515447&partnerID=8YFLogxK
U2 - 10.1039/b911179d
DO - 10.1039/b911179d
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AN - SCOPUS:70350515447
SN - 1463-9076
VL - 11
SP - 9653
EP - 9666
JO - Physical Chemistry Chemical Physics
JF - Physical Chemistry Chemical Physics
IS - 42
ER -