摘要
We present a new concise approach for normalizing m-photon-added squeezed state a^tmS（s）｜0〉≡｜r〉m and mphoton-subtracted squeezed state a^m S （ r ） ｜0〉） ≡ ｜r〉m, i.e., we construct the generating function ∑m=0^∞ t^m/m!m〈r｜r〉m and ∑m=0^∞ t^m/m!_m〈r｜r〉_m respectively, after calculating them and comparing the result with the standard form of generating function of Legendre polynomials Pm, we find m〈r｜r〉m=m!cosh^m rPm（cosh r）,amd _m〈r｜r〉_m=m! （-i sinh r）^ m pm （ i sinh r）, where r is the squeezing parameter.
We present a new concise approach for normalizing m-photon-added squeezed state a^tmS（s）｜0〉≡｜r〉m and mphoton-subtracted squeezed state a^m S （ r ） ｜0〉） ≡ ｜r〉m, i.e., we construct the generating function ∑m=0^∞ t^m/m!m〈r｜r〉m and ∑m=0^∞ t^m/m!_m〈r｜r〉_m respectively, after calculating them and comparing the result with the standard form of generating function of Legendre polynomials Pm, we find m〈r｜r〉m=m!cosh^m rPm（cosh r）,amd _m〈r｜r〉_m=m! （-i sinh r）^ m pm （ i sinh r）, where r is the squeezing parameter.
基金
Supported by the Specialized Research Fund for Doctoral Program of Higher Education, and the National Natural Science Foundation of China under Grant Nos 10775097 and 10947017/A05.
