N-TH ROOT OF HERMITE MATRIX AND ITS APPLICATION IN QUANTUM SYSTEMS

被引：0
|
作者：
Xu, Shi-Min [1 ,2 ]
Xu, Xing-Lei [1 ,2 ]
Jiang, Feng [1 ]
Li, Hong-Qi [1 ,2 ]
机构：
[1] Heze Univ, Dept Phys, Heze 274015, Shandong, Peoples R China
[2] Heze Univ, Key Lab Quantum Commun & Calculat, Heze 274015, Shandong, Peoples R China
来源：
MODERN PHYSICS LETTERS B | 2013年 / 27卷 / 22期
关键词：
Hermitian matrix; n-th root of matrices; coupling; unitary operator;
D O I：
10.1142/S0217984913501595
中图分类号：
O59 [应用物理学];
学科分类号：
摘要：
In this paper, the n-th root of a matrix is defined, and the explicit form of n-th root of an Hermitian matrix is given. A new method for diagonalizing quadratic Hamiltonians is proposed. Also, a class of quantum operators is induced by the linear transformation in configuration space, and its unitary properties and transformation behavior are studied. Our new method based on n-th root of matrices can develop the mathematical methods of quantum mechanics and quantum optics, and can also be applied to engineering, quantum optics and quantum fields states with squeezing properties, as well as the binomial field states.
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页数：9
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