Geodesic
Computation of the ground state energy of the Schrödinger equation by a Monte Carlo method
Mathematica Applicanda, Tome 49 (2021) no. 1, pp. 55-64.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The paper presents a new method of computing the ground state energy of the time-independent Schrödinger equation. The method is based on a local separation of variables: the Schrödinger equation is transformed to an equivalent system of local one-electron auxiliary equations which is used to derive an expression for the energy integral. The latter allows to calculate the ground-state energy of many-electron systems with the full inclusion of electron correlations. The multidimensional energy integrals are calculated using the Markov Chain Monte Carlo method. We provide benchmark results for two-electron systems which are in agreement with the accurate computations by the configuration interaction (CI) method.
DOI : 10.14708/ma.v49i1.7077
Classification : 81V45, 81-08, 65C05.
Mots-clés : quantum mechanics, Schr ̈odinger equation, Markov chain Monte Carlo, ground state energy, Metropolis-Hastings algorithm, local separation of variables. 
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     title = {Computation of the ground state energy of the {Schr\"odinger} equation by a {Monte} {Carlo} method},
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Adam Puchalski. Computation of the ground state energy of the Schrödinger equation by a Monte Carlo method. Mathematica Applicanda, Tome 49 (2021) no. 1, pp.  55-64. doi : 10.14708/ma.v49i1.7077. http://geodesic.mathdoc.fr/articles/10.14708/ma.v49i1.7077/

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