Wavelet transform in the context of quantum mechanics and new orthogonal property of mother wavelets in parameter space |
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| Authors: | Li-Yun Hu Hong-Yi Fan |
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| Affiliation: | 1. Department of Physics , Shanghai Jiao Tong University , Shanghai, China hlyun@sjtu.edu.cn;3. Department of Physics , Shanghai Jiao Tong University , Shanghai, China |
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| Abstract: | Based on the quantum mechanical version of wavelet transform (WT) W ψ f(μ,s)?=??ψ|U(μ,s)|?f?? Fan, H.Y.; Lu, H.L. Opt. Lett. 2006, 31, 407] we further prove Parseval theorem and inversion formula for WT in the context of quantum mechanics. The concise proof not only manifestly shows the merit of Dirac's representation theory, but also leads to a new orthogonal property of mother wavelets in parameter space. |
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| Keywords: | wavelet transform quantum mechanics Parseval theorem |
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