In this work, we study the position and momentum information entropies of multiple quantum well systems in fractional Schrödinger equations, which, to the best of our knowledge, have not so far been studied. Through a confining potential, their shape and number of wells (NOW) can be controlled by using a few tuning parameters; we present some interesting quantum effects that only appear in the fractional Schrödinger equation systems. One of the parameters denoted by the L_d can affect the position and momentum probability densities if the system is fractional (1 < α < 2). We find that the position (momentum) probability density tends to be more severely localized (delocalized) in more fractional systems (ie, in smaller values of α). Affecting the L_d on the position and momentum probability densities is a quantum effect that only appears in the fractional Schrödinger equations. Finally, we show that the Beckner Bialynicki‐Birula‐Mycieslki (BBM) inequality in the fractional Schrödinger equation is still satisfied by changing the confining potential amplitude V_conf, the NOW, the fractional parameter α, and the confining potential parameter L_d.

中文翻译：

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分数薛定ding方程中多量子阱系统的量子信息熵

在这项工作中，我们研究分数Schrödinger方程中的多个量子阱系统的位置和动量信息熵，据我们所知，到目前为止，尚未对其进行研究。通过限制电位，可以通过使用一些调整参数来控制孔的形状和数量（现在）。我们提出了一些有趣的量子效应，这些效应只出现在分数薛定ding方程组中。如果系统为分数（1 < α  <2），则由L _d表示的参数之一会影响位置和动量概率密度 。我们发现位置（动量）概率密度倾向于在更多的分数系统（即，较小的α值）中更严重地局部化（离域化））。影响大号_d上的位置和动量概率密度是仅出现在一个量子效应分数薛定谔方程。最后，我们表明，通过更改约束电位振幅V _conf，NOW，分数参数α和约束电位参数L _d，仍能满足分数Schrödinger方程中的贝克纳Bialynicki-Birula-Mycieslki（BBM）不等式。