标题： 使用量子代数框架的波尔兹曼系统相干态的直接方法 显示英文标题

标题： A direct approach to coherent states of billiards using a quantum algebra framework

摘要： 量子弹道是量子力学中的一个关键研究领域，提供了一个简单而强大的模型来研究复杂的量子特性。 虽然对量子系统的代数发展可以从一维可积模型追溯到量子群和广义海森堡代数（GHA）。 本工作的主要重点是将GHA扩展到量子弹道，展示其在可分离和不可分离弹道中的应用。 我们将该形式化方法应用于正方形弹道，首先生成具有特定量子数的一维相干态并探索它们的时间演化。然后，我们扩展这种方法以开发正方形弹道的二维相干态。 我们还展示了其在不可分离的等边三角形弹道中的适用性，描述了它们的代数生成器和相关的一维相干态。 显示英文摘要

摘要： Quantum billiards are a key focus in quantum mechanics, offering a simple yet powerful model to study complex quantum features. While the development of algebras for quantum systems is traced from one-dimensional integrable models to quantum groups and the Generalized Heisenberg Algebra (GHA). The primary focus of this work is to extend the GHA to quantum billiards, showcasing its application to separable and non-separable billiards. We apply the formalism to a square billiard, first generating one-dimensional coherent states with specific quantum numbers and exploring their time evolution.Then, we extend this approach to develop two-dimensional coherent states for the square billiards. We also demonstrate its applicability in a non-separable equilateral triangle billiard, describing their algebra generators and associated one-dimensional coherent states.