The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state repr...The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wave functions of harmonic oscillator are deduced.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475056 and 10647133 and the Research Foundation of the Education Department of Jiangxi Province under Grant No. [2007]22
文摘The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wave functions of harmonic oscillator are deduced.
