期刊
PHYSICAL REVIEW E
卷 80, 期 6, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.066706
关键词
eigenvalues and eigenfunctions; mathematical operators; matrix algebra; numerical analysis; quantum theory
资金
- Ministry of Science and Technological Development of the Republic of Serbia [OI14103]
- German Academic Exchange Service (DAAD)
- European Commission
In this paper, building on a previous analysis [I. Vidanovicacute, A. Bogojevicacute, and A. Belicacute, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.
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