シュレーディンガー方程式の格子法における限界突破：1次元・2次元・3次元量子問題に対するスパースNumerov法
This study presents a modified Numerov approach tailored for numerical solutions of Schrödinger's equation. A hierarchy of new stencil expressions for the Laplace operator was developed across one, two, and three dimensions, simplifying the standard Numerov scheme. By exploiting matrix sparsity, both memory requirements and computation time were substantially reduced, extending applicability to larger quantum systems. Validation was performed using harmonic and Morse potential problems in one and two dimensions. Vibrational frequencies of molecular hydrogen and water were computed with explicit inclusion of anharmonicity, mode-mode coupling, and nuclear quantum effects. Tunneling splitting in malonaldehyde was also evaluated as a representative two-dimensional problem.
Novel stencil expressions for the Laplace operator combined with sparse matrix techniques reduce memory and computational demands, enabling the Numerov method to handle larger quantum mechanical problems including molecular hydrogen vibrational analysis.
The delivery route is not clearly identifiable from this paper. For hydrogen intake, inhalation is the most efficient route; inhalation, however, carries explosion risk (empirical LFL of 10%; high-concentration devices are not recommended).
See also:
https://h2-papers.org/en/papers/27831582