  Generalized squeezing rotating-wave approximation (GSRWA) is proposed by
employing both the displacement and the squeezing transformations. A solvable
Hamiltonian is reformulated in the same form as the ordinary RWA ones. For a
qubit coupled to oscillators experiment, a well-defined
Schr\"{o}dinger-cat-like entangled state is given by the displaced-squeezed
oscillator state instead of the original displaced state. For the isotropic
Rabi case, the mean photon number and the ground-state energy are expressed
analytically with additional squeezing terms, exhibiting a substantial
improvement of the GSRWA. And the ground-state energy in the anisotropic Rabi
model confirms the effectiveness of the GSRWA. Due to the squeezing effect, the
GSRWA improves the previous methods only with the displacement transformation
in a wide range of coupling strengths even for large atom frequency.
