The solution of the Schrödinger equation in imaginary time by Green's function Monte Carlo. The rigorous sampling of the attractive Coulomb singularity

Douglas W. Skinner; Jules W. Moskowitz; Michael A. Lee; Paula A. Whitlock; K. E. Schmidt

doi:10.1063/1.449038

The solution of the Schrödinger equation in imaginary time by Green's function Monte Carlo. The rigorous sampling of the attractive Coulomb singularity

Douglas W. Skinner, Jules W. Moskowitz, Michael A. Lee, Paula A. Whitlock, K. E. Schmidt

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We present a new Green's function Monte Carlo method for solving for the ground state of the Schrödinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium-like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.

Original language	English (US)
Pages (from-to)	4668-4672
Number of pages	5
Journal	The Journal of chemical physics
Volume	83
Issue number	9
DOIs	https://doi.org/10.1063/1.449038
State	Published - Jan 1 1985
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy
Physical and Theoretical Chemistry

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10.1063/1.449038

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abstract = "We present a new Green's function Monte Carlo method for solving for the ground state of the Schr{\"o}dinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium-like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.",

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T1 - The solution of the Schrödinger equation in imaginary time by Green's function Monte Carlo. The rigorous sampling of the attractive Coulomb singularity

AU - Skinner, Douglas W.

AU - Moskowitz, Jules W.

AU - Lee, Michael A.

AU - Whitlock, Paula A.

AU - Schmidt, K. E.

PY - 1985/1/1

Y1 - 1985/1/1

N2 - We present a new Green's function Monte Carlo method for solving for the ground state of the Schrödinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium-like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.

AB - We present a new Green's function Monte Carlo method for solving for the ground state of the Schrödinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium-like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.

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The solution of the Schrödinger equation in imaginary time by Green's function Monte Carlo. The rigorous sampling of the attractive Coulomb singularity

Abstract

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