We study realizations generated by the original Weyl–Titchmarsh functions \(m_\infty (z)\) and \(m_\alpha (z)\). It is shown that the Herglotz–Nevanlinna functions \((-\,m_\infty (z))\) and \((1/m_\infty (z))\) can be realized as the impedance functions of the corresponding Shrödinger L-systems sharing the same main dissipative operator. These L-systems are presented explicitly and related to Dirichlet and Neumann boundary problems. Similar results but related to the mixed boundary problems are derived for the Herglotz–Nevanlinna functions \((-\,m_\alpha (z))\) and \((1/m_\alpha (z))\). We also obtain some additional properties of these realizations in the case when the minimal symmetric Shrödinger operator is non-negative. In addition to that we state and prove the uniqueness realization criteria for Shrödinger L-systems with equal boundary parameters. A condition for two Shrödinger L-systems to share the same main operator is established as well. Examples that illustrate the obtained results are presented in the end of the paper.

我们研究由原始的Weyl–Titchmarsh函数\（m_ \ infty（z）\）和\（m_ \ alpha（z）\）生成的实现。结果表明，可以将Herglotz–Nevanlinna函数\（（-\，m_ \ infty（z））\）和\（（1 / m_ \ infty（z））\）作为相应的Shrödinger的阻抗函数来实现L系统共享相同的主要耗散算子。这些L系统是明确提出的，并且与Dirichlet和Neumann边界问题有关。对于Herglotz–Nevanlinna函数\（（-\，m_ \ alpha（z））\）和\（（1 / m_ \ alpha（z））\）得出相似的结果，但与混合边界问题有关。在最小对称Shrödinger运算符为非负数的情况下，我们还获得了这些实现的其他一些属性。除此之外，我们陈述并证明具有相等边界参数的ShrödingerL系统的唯一性实现标准。还建立了两个ShrödingerL系统共享同一主算子的条件。本文末尾提供了说明获得的结果的示例。