Some properties of the states engendered by the action of photon creation and annihilation operator on a squeezed vacuum state
Hong-Yi Fan, Zhongxi Zhang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
We study some properties of the states a+mS(r)0> and amS(r)0> (S(r) equals e-$ (a(superscript 2-a+2)) which are engendered by the excitations and de-excitations on a squeezed vacuum state, respectively. Using the mathematical induction method, we easily show that such states are normalized as two different forms of Legendre polynomials of squeezing parameter r. The Wigner functions of these states are also derived and analyzed.