期刊
PHYSICAL REVIEW E
卷 80, 期 6, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.066705
关键词
error analysis; mathematical operators; quantum theory
资金
- Ministry of Science and Technological Development of the Republic of Serbia [OI141035]
- German Academic Exchange Service (DAAD)
- European Commission
We analyze the method for calculation of properties of nonrelativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing Delta. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with 1/Delta(2). As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the follow up paper [I. Vidanovicacute, A. Bogojevicacute, A. Balazc, and A. Belicacute, Phys. Rev. E 80, 066706 (2009)] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.
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