Numerical solution of heisenberg model

[meygolbostan]

Homework Statement

Hi! I'm studying a computational physics course and have been ok so far but the newest problem relates to quantum mechanics and I am struggling to understand... I would really appreciate it if someone could help me . i want to solve the Heisenberg hamiltonian for 10 particels,i can make hamiltonian matrix and basis vector but i am struggling to find eigenvalues and eigenvectors.i have problem in programming.
i have solved laplace and poisson equation with jacobi method but i think this problem is diffrent.

Homework Equations

The Attempt at a Solution

 

[BigJDubs]

The best way to approach this problem would be to first find the Hamiltonian matrix for the 10 particles, which can be done using the Heisenberg equation. Once you have the Hamiltonian matrix, you can then use numerical methods such as the Jacobi method to solve for the eigenvalues and eigenvectors. Additionally, you may want to consider using other numerical methods such as the Lanczos algorithm or the Davidson algorithm.