四元束缚态
Quaternionic bound states
摘要：
研究了有限深四元数球形方势阱中零角动量的束缚态解。正如在标准量子力学中一样，这种解只适用于能量的离散值。乍一看，它似乎是连续性条件施加了非常严格的约束的能量本征值，因此，没有束缚态的能量值低于纯四元数潜力的预期。然而，仔细的分析表明，纯四元数势不删除束缚态。将这些新解与试探复势的束缚态解进行比较也是有趣的。本文提出的研究代表了一个初步的一步，充分了解的作用，四元数势可以发挥量子力学。作者特别感兴趣的是分析限制波包和隧道时间在这个新的量子理论制定。
英文摘要：
We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance, it seems that the continuity conditions impose a very restrictive constraint on the energy eigenvalues and, consequently, no bound states was expected for energy values below the pure quaternionic potential. Nevertheless, a careful analysis shows that pure quaternionic potentials do not remove bound states. It is also interesting to compare these new solutions with the bound state solutions of the trial-complex potential. The study presented in this paper represents a preliminary step towards a full understanding of the role that quaternionic potentials could play in quantum mechanics. Of particular interest for the authors it is the analysis of confined wave packets and tunnelling times in this new formulation of quantum theory.
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