https://www.quanty.org/ 2026-04-30T18:06:45+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T02:29:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/model_examples_from_physics/harmonic_oscillator?rev=1763605783&do=diff Harmonic oscillator This example solves the Harmonic oscillator numerically on a basis of plane waves. -- solves the Harmonic oscillator H = -1/2 (d^2/dx^2) + 1/2 x^2 -- on a basis of complex plane waves -- the plane wave basis assumes a periodicity, this length is: a = 20 -- maximum k (ikmax * 2 * pi/a) ikmax = 60 -- each plane wave is a basis "spin-orbital" k runs from -kmax to kmax, including 0, i.e. the number of basis "spin-orbitals" is: NF = 2 * ikmax + 1 -- integration steps dxint = 0.00… text/html 2025-11-20T02:29:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/model_examples_from_physics/hubbard_model_on_a_dimer?rev=1763605783&do=diff Hubbard model on a dimer This example shows the effect of inter-site correlations in a two site Hubbard model, aka a H$_2$ molecule on the smallest basis possible. The solution of this problem is analytically known. The large $U$ limit is known as the Heither-London approximation.model_examples_from_physics index text/html 2025-11-20T02:29:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/model_examples_from_physics/start?rev=1763605783&do=diff Model examples from physics In order to understand what correlations do to your system it is often good to look at model calculations. Here we present several examples of simple model systems. Table of contents model_examples_from_physics index