Universal invariants of quantum-mechanical and optical systems

被引：0

作者：

Dodonov, Victor V. ^{[1
,3
]}

Man'ko, Olga V. ^{[2
]}

机构：

[1] Departamento de Física, Univ. Federal de São Carlos, 13565-905 Sao Carlos, Sao Paulo, Brazil

[2] P. N. Lebedev Physics Institute, Leninsky Prospect 53, 117924 Moscow, Russia

[3] P. N. Lebedev Physics Institute, Moscow Inst. of Phys. and Technology, Dolgoprudny, Moscow region 141700, Russia

来源：

Journal of the Optical Society of America A: Optics and Image Science, and Vision | 2000年 / 17卷 / 12期

关键词：

Algebra - Eigenvalues and eigenfunctions - Hamiltonians - Quantum theory;

D O I：

10.1364/josaa.17.002403

中图分类号：

学科分类号：

摘要：

We give a brief review of the theory of quantum and optical universal invariants, i.e., certain combinations of the second- and higher-order moments (variances) of quantum-mechanical operators or the transverse phase-space coordinates of optical paraxial beams that are preserved in time (or along the axis of the beam) independently of the concrete form of the coefficients of the Hamiltonian or the parameters of the optical system, provided that the effective Hamiltonian is either a generic quadratic form of the generalized coordinate-momenta operators or a linear combination of generators of certain finite-dimensional algebras. Using the phase-space representation of quantum mechanics (paraxial optics) in terms of the Wigner function, we elucidate the relation between the quantum invariants and the classical universal integral invariants of Poincaré and Cartan. The specific features of the Gaussian beams are discussed as examples. © 2000 Optical Society of America.

引用

页码：2403 / 2410