Solving Schrödinger Equation Using MATLAB's Built-in eigs Function
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Resource Overview
Practical implementation of MATLAB's built-in eigs function for solving Schrödinger equation, featuring simple code structure, high accuracy, and wave number results matching analytical solutions
Detailed Documentation
In this article, we demonstrate how to solve the Schrödinger equation using MATLAB's built-in eigs function. The implementation leverages sparse matrix eigenvalue computation where eigs efficiently calculates a specified number of eigenvalues and eigenvectors for large sparse systems. The code structure is straightforward and user-friendly, making it accessible even for beginners. The algorithm discretizes the Hamiltonian operator into a sparse matrix format, then uses Arnoldi iteration methods through eigs to compute eigenstates. This approach maintains high accuracy with computational results showing perfect agreement with analytical solutions for wave numbers. The method ensures reliable solutions for quantum mechanical systems while providing precise numerical results. Overall, this MATLAB implementation offers a robust and recommended approach for solving Schrödinger equations efficiently.
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