For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （...For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.展开更多
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...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.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070358009)
文摘For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.
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)
文摘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.
