理论物理通讯：英文版

Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator

Fan, Hong-Yi, LU LU, Hailiang

Published Jan 1, 2006• 1 citation

Abstract

我们证明二模式的夫累Ｘ尔操作员只是的时间依赖者 Hamiltonian 管理的 thetime 进化的单一的操作员以展出苏(1,1 ) 的方法正规操作员的二次的联合创作了代数学。这是为在古典阶段空间从 preassigned 时间进化获得 thetime 依赖的 Hamiltonian 的一条途径，与 Lewis-Riesenfeld 相对照的一条途径“ s 对待 time-dependentharmonic 振荡器的不变的操作符理论。

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理论物理通讯：英文版

Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator

Fan, Hong-Yi, LU LU, Hailiang

Published Jan 1, 2006• 1 citation

OpenAlex

Abstract

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Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having

\mathcal{PT}

𝒫𝒯 symmetry

We apply the techniques of canonical transforms to equations of the type

\left[ {A( t )\mathbb{P}^2 + B( t )\{ \mathbb{P}\mathbb{Q} + \mathbb{Q}\mathbb{P} \} + C( t )\mathbb{Q}^2 + D( t )\mathbb{Q} + E( t )\mathbb{P} + F( t )\mathbb{1}} \right]\psi ( q,t ) = - i\partial _t \psi ( q,t ),

where

\mathbb{Q}

and

\mathbb{P}

are the quantum position and momentum operators. The time-dependent parameters of the

{\text{W}} \wedge {\text{SL}}( {{\text{2,}}R} )

evolution operator are found through linear differential equations. In terms of these we give explicitly the Green’s function, all separating coordinates and similarity solutions of the equation. We analyze the behavior of Gaussian and coherent-state initial conditions in closed form and present a new interpretation of all the Lewis-Riesenfeld constants of motion.