摘要
Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.
Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.
基金
supported by the National Natural Science Foundation of China (Grant No. 10574060)
the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)
the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
