The ground-state energy and the average number of virtual phonons around the electron in a parabolic quantum dot for the entire range of the electron-phonon coupling constant are obtained using the single-mode squeezed-state variational approach.The variational approach we applied is based on two successive canonical transformations and using a displaced-oscillator type unitary transformation to deal with the bilinear terms which are usually neglected.In order to study the relationship between the ground-state energy and the average number of virtual phonons around the electron of a polaron in a parabolic quantum dot with the electron-LO-phonon coupling constant and the confinement length,numerical calculations are carried out in the electron-LO-phonon strong-and weak-coupling regions.
