Quantum dynamics of a plane pendulum
Quantum dynamics of a plane pendulum
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平面摆的量子动力学
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
B. Schmidt
中科院分区：
文献类型：
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作者：
M. Leibscher;B. Schmidt
基于表现为驻波函数的Mathieu函数，发展了一种研究平面摆量子动力学的半解析方法。含时薛定谔方程求解的谐振子的相干态和压缩态的摆动类似物，诱导的周期势能函数的瞬时变化。相干摆动状态之间的小位移的谐波限制和倒立摆的限制进行了讨论，而压缩摆动状态的振动和自由旋转运动之间插入。在后者的情况下，充分和分数的复苏，以及时空结构的概率密度（量子地毯）的时间演化进行了定量分析。平均取向的相应表达式推导出在时间的马蒂厄函数。对于周期性双阱势，对于形成基态隧穿二重态的奇、偶初始态，我们发现了不同的恢复方案和不同的量子地毯。平均排列的时间演化允许具有不同宇称的状态的分离。外部（旋转）和内部（扭转）运动的分子诱导强激光场的影响进行了讨论。
A semi-analytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schrodinger equation is solved for pendular analogues of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time-evolution of the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed.