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

1985 ◽  
Vol 83 (9) ◽  
pp. 4668-4672 ◽  
Author(s):  
Douglas W. Skinner ◽  
Jules W. Moskowitz ◽  
Michael A. Lee ◽  
Paula A. Whitlock ◽  
K. E. Schmidt
Keyword(s):  
Monte Carlo ◽  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Schrodinger Equation ◽  
Imaginary Time ◽  
Coulomb Singularity ◽  
Green's Function Monte Carlo

PATH INTEGRAL CALCULATION OF GREEN’S FUNCTION FOR SCHRÖDINGER EQUATION IN UNITARY GAUGE

1992 ◽  
Vol 07 (31) ◽  
pp. 7775-7786
Author(s):  
L. ROZANSKY
Keyword(s):  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Preexponential Factor ◽  
Unitary Gauge ◽  
Gauge Fixing

Green’s function of Schrödinger equation is represented as a time-reparametrization invariant path integral. Unitary gauge fixing enables us to get the WKB preexponential factor without calculating determinants of operators containing derivatives.

scholarly journals The Use of Parameter-Free Correlation Functions in Green's Function Monte Carlo Simulations of Small Electronic Systems

1997 ◽  
Vol 52 (11) ◽  
pp. 793-802 ◽  
Author(s):  
C. Mecke ◽  
F. F. Seelig
Keyword(s):  
Monte Carlo ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
High Performance ◽  
Limited Range ◽  
Electronic Energy ◽  
Simple Expression ◽  
Electronic Systems ◽  
Green's Function Monte Carlo

Abstract Using an old formulation for correlation functions with correct cusp-behaviour, the Schrödinger equation transforms to a new differential equation which provides a very simple expression for the local electronic energy with limited range. This, together with the simplicity of the formulation promises a high performance in Green's function Monte Carlo (GFMC) simulations of small electronic systems. The behaviour of the local energy is studied on a few simple examples because the variance of this function determines the quality of the results in the GFMC methods. Calculations for one-and two-electron systems are presented and compared with results from well-known functions. The form of the function is then extended to systems with more than two electrons. Results for the Be atom are given and the extension to larger electronic systems is discussed.

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