纠缠相互作用粒子的q-广义薛定谔方程的解
Solutions for a q-generalized Schrödinger equation of entangled interacting particles
摘要：
本文研究了Nobre等人提出的$q-$广义薛定谔方程的含时解。106，140601（2011）]。在这里，我们调查的情况下，两个自由粒子的情况下，两个粒子受到一个Moshinsky型势与时间相关的系数。我们对不同的$q$参数值给出了解析解和数值解，并证明了通常的薛定谔方程在$q\rightarrow 1$的极限下得到了恢复.观察到$q=2$的有趣行为，其中波函数显示环状形状，表明颗粒的结合行为。与以前报道的单粒子情况下的结果不同，在$q=3$的情况下，冻结态只出现在波函数参数的特殊组合中。
英文摘要：
We report on the time dependent solutions of the $q-$generalized Schrödinger equation proposed by Nobre et al. [Phys. Rev. Lett. 106, 140601 (2011)]. Here we investigate the case of two free particles and also the case where two particles were subjected to a Moshinsky-like potential with time dependent coefficients. We work out analytical and numerical solutions for different values of the parameter $q$ and also show that the usual Schrödinger equation is recovered in the limit of $q\rightarrow 1$. An intriguing behavior was observed for $q=2$, where the wave function displays a ring-like shape, indicating a bind behavior of the particles. Differently from the results previously reported for the case of one particle, frozen states appear only for special combinations of the wave function parameters in case of $q=3$.
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