Treatment of the Schrödinger equation through a Monte Carlo method based upon the generalized Feynman-Kac formula

1986 ◽  
Vol 43 (5-6) ◽  
pp. 797-801 ◽  
Author(s):  
Michel Caffarel ◽  
Pierre Claverie
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Schrodinger Equation

A quantum method for dynamic nonlinear programming technique using Schrödinger equation and Monte Carlo approach

2018 ◽  
Vol 32 (30) ◽  
pp. 1850374 ◽  
Author(s):  
Amandeep Kaur ◽  
Satnam Kaur ◽  
Gaurav Dhiman
Keyword(s):  
Monte Carlo ◽  
Quantum Computing ◽  
Nonlinear Programming ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Nonlinear Problem ◽  
Schrodinger Equation ◽  
Programming Technique ◽  
Quantum Method ◽  
Speed Up

The power of quantum computing may allow for solving the problems which are not practically feasible on classical computers and suggest a considerable speed up to the best known classical approaches. In this paper, we present the contemporary quantum behaved approach which is based on Schrödinger equation and Monte Carlo method. The three basic steps of proposed technique are also mathematically modeled and discussed for effective movement of particles. The performance of the proposed approach is tested for solving the dynamic nonlinear problem. Experimental results reveal the supremacy of proposed approach for solving the nonlinear problem as compared to other approaches.

A NONADIABATIC QUANTUM MECHANICAL MONTE CARLO METHOD

2002 ◽  
Vol 13 (07) ◽  
pp. 909-915
Author(s):  
A. M. MAZZONE
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Efficient Solution ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Classical Dynamics ◽  
Hartree Fock

The problem addressed by this study is an efficient solution of the multi-particle time-dependent Schrödinger equation to be used under nonadiabatic conditions. To this purpose a solution combining classical dynamics for the nuclei and a quantum mechanical Monte Carlo method for the electrons is suggested as a practically feasible approach. As a show-case example, the method is applied to the evaluation of the ground state of H, He, H2 and H3 whose energy and structure is also obtained from stationary Hartree–Fock calculations.

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