New Approach for Normalizing Photon-Added and Photon-Subtracted Squeezed States

We present a new concise approach for normalizing. m-photon-added squeezed state a(dagger m)S(r)vertical bar 0 > equivalent to vertical bar r >(m) and m-photon-subtracted squeezed state a(m) S(r)vertical bar 0 > equivalent to vertical bar r >((m) under bar), i.e., we construct the generating function Sigma(infinity)(m=0) t(m)/m!m < r vertical bar r >(m) and Sigma(infinity)(m=0) t(m)/m!(m) under bar < r vertical bar r >((m) under bar) respectively, after calculating them and comparing the resut with the standard form of generating function of Legendre polynomials P-m, we find m < r vertical bar r >(m) = m!cosh(m)rP(m)(cosh r), and ((m) under bar)< r vertical bar r >((m) under bar) = m!(-i sinh r)(m) P-m(i sinh r), where r is the squeezing parameter.