Calculation of Gaussian Perturbation on Two Harmonic Oscillators by Virtue of Entangled State Representation
Liyun Hu, Nanrun Zhou, Fan Hong-Yi · Communications in Theoretical Physics · 2007
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 wavefunctions of harmonic oscillator are deduced.