Numerical solution of the Schrödinger equation using Neural Networks in Python

The motion of quantum mechanical systems in physical sciences is described by partial differential equations, usually of second order with respect to spatial coordinates. The required solutions of the time-dependent type of equations are, in general, functions of the temporal variable t and the stat...

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Bibliographic Details
Published in:Journal of physics. Conference series 2024-02, Vol.2701 (1), p.12133
Main Authors: Gkrepis, A., Kosmas, O., Vlachos, D., Kosmas, T.
Format: Article
Language:English
Subjects:
Mechanical systems
Neural networks
Partial differential equations
Physical sciences
Quantum mechanics
Schrodinger equation
State vectors
Time dependence
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Summary:The motion of quantum mechanical systems in physical sciences is described by partial differential equations, usually of second order with respect to spatial coordinates. The required solutions of the time-dependent type of equations are, in general, functions of the temporal variable t and the state vectors determining the positions of the system’s particles at the time t. Only a small number, however of those differential equations can however be solved analytically, while the majority of them must be solved numerically by applying specific very advanced integration techniques. Among these equations, the fundamental Schrödinger equation offers great insight towards numerical solving. In this work we present an effective method that solves numerically the time-independent Schrodinger equation on the basis of neural networks techniques. Analytical and numerical results for the radial part of this equation with the corresponding energies are then compared so as to estimate the performance of our method.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/2701/1/012133