物质波包串的传播、呼吸和跃迁
Propagation, breathing and transition of matter-wave packet trains
摘要：
我们找到了一组新的量子谐振子的精确解，它描述了一些波包序列，其平均能量与谐振子的量子能级和经典能量都成正比。波包列的中心可以像频率为$ω$的经典谐振子一样振荡。列的宽度和宽度可以随着频率$2 ω$同时改变，作为呼吸器的阵列。在一定的微扰下，波包串可以在不同量子数的态之间跃迁。我们用解析和数值方法证明了波包序列可以严格地拟合Strecher等人在Nature 417，150（2002）中观测到的物质波孤子序列。当波包以更大的振幅呼吸时，它们表现出物质波的周期性崩溃和复苏。
英文摘要：
We find a set of new exact solutions of a quantum harmonic oscillator, which describes some wave-packet trains with average energy being proportional to both the quantum level and classical energy of the oscillator. Center of the wave-packet trains may oscillate like a classical harmonic oscillator of frequency $ω$. Width and highness of the trains may change simultaneously with frequency $2 ω$ as an array of breathers. Under some perturbations the wave-packet trains could transit between the states of different quantum numbers. We demonstrate analytically and numerically that the wave-packet trains can be strictly fitted to the matter-wave soliton trains observed by Strecher et al. and reported in Nature 417, 150(2002). When the wave-packets breathe with greater amplitudes, they show periodic collapse and revival of the matter-wave.
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