Dirac delta-function potential is widely studied in quantum mechanics because it usually can be exactly solved and at the same time is useful in modeling various physical systems. Here we study a system of delta-potential trapped spin–orbit coupled cold atoms. The spin–orbit coupled atomic matter wave has two kinds of evanescent modes, one of which has a pure imaginary wavevector and is an ordinary evanescent wave; while the other with a complex number wave vector is recognized as an oscillating evanescent wave. We identified the eigenenergy spectra and the existence of bound states in this system. The bound states can be constructed analytically using the two kinds of evanescent modes and we found that they exhibit typical features of stripe phase, separated phase or zero-momentum phase. In addition to that, the properties of semi-bound states are also discussed, which is a localized wave packet on a plane wave background.

中文翻译：

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Dirac三角函数势中自旋轨道耦合冷原子的束缚态

狄拉克δ函数势在量子力学中得到了广泛的研究，因为它通常可以被精确地求解，同时也可以用于对各种物理系统进行建模。在这里，我们研究了一个由δ电位捕获的自旋轨道耦合的冷原子组成的系统。自旋轨道耦合原子物质波具有两种of逝模式，其中一种具有纯虚波矢量，是普通的e逝波。而另一个具有复数波向量的波被认为是振荡的van逝波。我们确定了本征能谱和该系统中束缚态的存在。可以使用两种of逝模式解析地构建结合态，我们发现它们表现出条纹相，分离相或零动量相的典型特征。在此之上，