半线库仑势的信息论性质
Information-Theoretic Properties of the Half-Line Coulomb Potential
摘要：
半线一维库仑势可能是最简单的D维模型，它的物理解已被证明能成功地描述里德伯原子在外场中的行为和液氦中表面态电子的动力学，在模拟量子计算机的构建等领域具有潜在的应用价值。在这里，我们调查的扩展和uncertaintylike属性的基态和激发态的对数测度和信息论长度的Renyi，香农和Fisher类型的装置，所以，远远超出海森堡措施。特别是，费舍尔长度（这是一个本地量的内部混乱）被证明是适当的措施，我们的系统在位置和动量空间的不确定性。此外，一个给定的物理状态的位置费歇尔长度不仅与其相关波函数的节点数成正比，而且遵循平方根能量定律。
英文摘要：
The half-line one-dimensional Coulomb potential is possibly the simplest D-dimensional model with physical solutions which has been proved to be successful to describe the behaviour of Rydberg atoms in external fields and the dynamics of surface-state electrons in liquid helium, with potential applications in constructing analog quantum computers and other fields. Here, we investigate the spreading and uncertaintylike properties for the ground and excited states of this system by means of the logarithmic measure and the information-theoretic lengths of Renyi, Shannon and Fisher types; so, far beyond the Heisenberg measure. In particular, the Fisher length (which is a local quantity of internal disorder) is shown to be the proper measure of uncertainty for our system in both position and momentum spaces. Moreover the position Fisher length of a given physical state turns out to be not only directly proportional to the number of nodes of its associated wavefunction, but also it follows a square-root energy law.
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