共查询到20条相似文献,搜索用时 312 毫秒
1.
推广了量子力学中关于对称性的分析,与对称性相关的守恒量相应地推广为含时守恒量;证明了单粒子(包括相对论情况)在静态均匀磁场和含时线性势中运动具有空间平移不变性;求出了波函数的变换关系和相应的含时守恒量. 相似文献
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用扩展Prelle-Singer法(扩展P-S法)求三自由度二阶非线性耦合动力学系统的守恒量,得到了6个积分乘子满足的确定方程、约束方程和守恒量的一般形式,并讨论了确定积分乘子的方法.最后,用扩展P-S法求得了三质点Tada晶格问题的两个守恒量. 相似文献
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将扩展Prelle-Singer法(扩展P-S法)用于求x=Ф1(x,y),y=Ф2(x,y)类型的二阶非线性耦合动力学系统的守恒量,得到了积分乘子满足的微分方程与守恒量的一般形式,并讨论所得守恒量的Noether对称性与Lie对称性.最后用扩展P-S法求得了四次非谐振子系统的两个守恒量,并讨论了系统的对称性. 相似文献
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研究一类动力学方程的Mei对称性的定义和判据,由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时,也可找到一类新型守恒量. 相似文献
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采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量.
关键词:
两自由度弱非线性耦合系统
近似Lie对称性
近似守恒量 相似文献
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Jeong Ryeol Choi 《Pramana》2004,62(1):13-29
By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator.
The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai
oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude
of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant
frequency oscillates with a large amplitude, even after a sufficient time elapse. 相似文献
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将对双振子系统简正振动的解耦分析运用于三振子和四振子系统,分析了三振子和四振予系统的筒正振动解耦的方式,并给出系统简正振动频率. 相似文献
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C. P. Burgess 《Pramana》1995,45(1):47-63
Bound state population dynamics in a diatom modelled by an appropriate Morse oscillator with a time-dependent well-depth is
investigated perturbatively both in the absence and presence of high intensity radiation. For sinusoidally oscillating well-depth,
the population of themth bound vibrational level,P
mm(t), is predicted to be a parabolic function of the amplitude of the oscillation of the well-depth (ΔD
0) at a fixed laser intensity. For a fixed value of ΔD
0,P
mm(t) is also predicted to be quadratic function of the field intensity (ɛ
0). Accurate numerical calculations using a time-dependent Fourier grid Hamiltonian (TDFGH) method proposed earlier corroborate
the predictions of perturbation theory. As to the dissociation dynamics, the numerical results indicate that the intensity
threshold is slightly lowered if the well-depth oscillates. Possibility of the existence of pulse-shape effect on the dissociation
dynamics has also been investigated. 相似文献
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本文建立了分数阶可停振动系统, 其可停振动状态的改变对周期策动力敏感, 对零均值随机微小扰动不敏感, 这事实上为周期未知微弱信号检测提供了一种新的高效检测方法和判别标准. 与现有的利用混沌系统的大尺度周期状态变化检测周期未知弱信号的方法 需逐一尝试设置不同频率内置信号以便期望与待检周期信号发生共振不同, 利用分数阶可停振动系统的可停振动状态变化检测周期未知微弱信号的方法, 除了同样具有因为状态变化对周期信号的敏感性而能够实现极低检测门限的特点外, 还具有混沌系统信号检测所不具有的优点: 1)无需预先估计待检信号的周期; 2)无需计算系统状态的临界阈值; 3)可停振动状态可由本文设计的指数波动函数可靠地进行判断; 4)通过系统微分阶数的变化, 将检测系统层次化, 从而可得到比整数阶检测系统更低的检测门限, 特别是在色噪声环境下, 通过选取合适的微分阶数, 基于分数阶可停振动系统的微弱周期信号检测法能够大幅度的降低检测门限, 在本文的仿真试验中, 检测门限可达-182 dB.
关键词:
分数阶非线性系统
Duffing振子
弱信号检测 相似文献
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行波管再生反馈振荡器是一种新型太赫兹源器件.基于560GHz折叠波导慢波结构,对此类器件的工作原理与物理模型进行分析阐述.采用非线性互作用模型对行波管再生反馈振荡器进行详细振荡过程模拟.模拟结果显示,在550—600GHz频率下可以获得稳态振荡频率,并在560GHz处获得最大单频输出功率.结果同时表明,振荡频率随电子注电压发生跳变现象,并简要分析了其产生原因. 相似文献
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提出并验证了一种有源环形谐振腔辅助滤波的光电振荡器. 它利用有源环形谐振腔提供的高Q光学梳状频率响应特性, 对振荡器中的光信号模式进行选择, 能有效地提高输出信号的边模抑制比, 获得光电振荡器的单模输出. 理论上, 对光电振荡器的起振模式以及有源腔的频率响应进行了分析, 仿真结果表明有源环形谐振腔的辅助滤波有利于光电振荡器的边模抑制和单模输出. 在实验上, 通过对比验证了理论的预期结果, 并最终得到中心频率为20 GHz, 边模抑制比为58.83 dB, 在频偏10 kHz处相位噪声为-97 dBc/Hz的单模信号输出. 该方案保留了已有光电振荡器边模抑制方法的优势, 实现方法上更加简便, 在工作带宽和可调谐性方面具备良好的灵活性. 相似文献
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The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schrödinger cat states defined as an eigenstate of $\hat{K}_{-}^{2}The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode
time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schr?dinger
cat states defined as an eigenstate of
are also studied. We applied our development to two-mode Caldirola-Kanai oscillator which is a typical example of the time-dependent
quadratic Hamiltonian system. The time evolution of the quadrature distribution for the probability density in the coherent
states are analyzed for the two-mode Caldirola-Kanai oscillator by plotting relevant figures. 相似文献
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For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtained as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space. 相似文献
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受与速度平方成正比的力的变频率谐振子(THOFQV)可以用一个适当的Lagrangian量来描述,可以求出THOFQV的普遍解.再利用不变量算子求解该系统的Schrdinger方程,得到本征函数和本征值.
关键词:
谐振子
不变量
本征函数
本征值 相似文献
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By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for someparametric moving boundaries as well. 相似文献