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Acta Physica Sinica

Wavelet transform of coherent state

Hai-jun Yu, Jian-ming Du, Xiulan Zhang

Published Jan 1, 2012• 3 citations
Publisher

Abstract

Two new mother wavelets are constructed on the basis of the quantum mechanics of classical wavelet transform. Based on that, the wavelet transform of coherent state and particle number state is studied with the technique of integration within an ordered product, and the wavelet transform from coherent state to particle number state is obtained by numerical calculation.

DOI
10.7498/aps.61.164205

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理论物理通讯：英文版•Jan 1, 2004•0 citations
Two new mother wavelets are constructed on the basis of the quantum mechanics of classical wavelet transform. Based on that, the wavelet transform of coherent state and particle number state is studied with the technique of integration within an ordered product, and the wavelet transform from coherent state to particle number state is obtained by numerical calculation.
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.
In the context of quantum mechanics we employ the technique of integration within an ordered product of operators to recast the classical wavelet transform to a squeezing-displacing transform between the mother wavelet vector and the state vector to be transformed. In this way we propose the wavelet-transform spectrum for quantum optical states. For some typical states we obtain numerical results which imply that the spectrum can be used to recognize a variety of quantum optical states, and the inverse wavelet transform has the possibility to play a role in quantum state engineering.
Abstract By using the technique of integral within an ordered product of operators, we recast classical wavelet transform to a matrix element of the squeezing‐displacing operator U (μ, s ) between the mother wavelet vector 〈ψ| and the state vector | f 〉 to be transformed, i.e., we propose that 〈ψ| U (μ, s )| f 〉 can be considered as a new kind of spectrum for analyzing the quantum state | f 〉. In this way, we propose the wavelet‐ transform spectrum for quantum chemical states. As an example, we carry out the numerical calculation of wavelet‐transform spectrum for the binomial state. It seems to us that this kind of spectrum can be used to recognize a variety of quantum chemical states. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012