Wavelet matrix operations and quantum transforms

Hiromasa Ohnishi, Hideaki Matsueda, Linlin Zheng

FANHong-Yi, LǖJian-Feng

Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum mechanics. In this way many quantum optical states'wavelet transform can be easily derived.

Hai-Sheng Li, Guiqiong Li, Haiying Xia

Fan Hong‐Yi, Jianfeng Lu

Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum mechanics. In this way many quantum optical states' wavelet transform can be easily derived.

Jun Song, Ye‐Jun Xu, Fan Hong‐Yi

In the context of quantum mechanics the classical wavelet transform of a function f with the mother wavelet can be recast into a matrix element of the squeezing-displacing operator U(,s) as 〈|U(,s) |f〉. The technique of integral within an ordered product of operators is used to support this theory. Based on this, wavelet transforms are done for even- and odd-binomial states, and the corresponding numerical calculation leads to the spectrum of wavelet transform, which is helpful for recognizing the difference between even- and odd-states.

Hai-Sheng Li, Ping Fan, Haiying Xia +1 more