无限量子透镜势的基态能量的生成界
Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential
摘要：
基于矩的方法已经产生了有效的多尺度量化算法来解决奇异摄动/强耦合问题。其中之一，特征值矩法（EMM），由汉迪等人（物理评论快报。{ \bf 55}，931（1985）;同上，{ \bf 60}，253（1988 b）），一旦已知相关波函数的特征特性，就产生到特定离散状态能量的收敛下限和上限。这种方法对于多维玻色子基态问题特别有效，因为相应的波函数必须具有一致的特征，并且可以取为正的。尽管如此，绝大多数研究的问题都是在无界域上。无限量子透镜势中的电子的重要问题定义了EMM到紧凑域上定义的系统的具有挑战性的扩展。我们在这里调查，并引入新的修改传统的EMM形式主义，促进其适应性所需的边界条件。
英文摘要：
Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging lower and upper bounds to a specific discrete state energy, once the signature property of the associated wavefunction is known. This method is particularly effective for multidimensional, bosonic ground state problems, since the corresponding wavefunction must be of uniform signature, and can be taken to be positive. Despite this, the vast majority of problems studied have been on unbounded domains. The important problem of an electron in an infinite quantum lens potential defines a challenging extension of EMM to systems defined on a compact domain. We investigate this here, and introduce novel modifications to the conventional EMM formalism that facilitate its adaptability to the required boundary conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
