On Quantum Representation of the Linear Canonical Wavelet Transform

被引：10
|
作者：
Srivastava, H. M. [1 ,2 ,3 ]
Shah, Firdous A. [4 ]
Teali, Aajaz A. [4 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
[3] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan
[4] Univ Kashmir, Dept Math, South Campus, Anantnag 192101, Jammu & Kashmir, India
来源：
UNIVERSE | 2022年 / 8卷 / 09期
关键词：
wavelet; linear canonical transform; quantum states; Dirac representation; inversion formula; MOTHER WAVELETS; MECHANICS;
D O I：
10.3390/universe8090477
中图分类号：
P1 [天文学];
学科分类号：
0704 ;
摘要：
For the efficient identification of quantum states, we propose the notion of linear canonical wavelet transform in the framework of quantum mechanics. Using the machinery of Dirac representation theory and integration within an ordered product of operators, we recast the linear canonical wavelet transform to a matrix element of the squeezing-displacing operator u (mu, s) K-M between analyzing vector <psi vertical bar and two-mode quantum state vector vertical bar f > to be transformed. We also derive the inner product relation and inversion formula for the linear canonical wavelet transform in the realm of quantum mechanics. Lastly, we present an explicit example for the lucid implementation of linear canonical wavelet transform in identifying the quantum states.
引用
收藏
页数：11
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