2D Density of States Calculator

A Python tool for the exact calculation of the density of states (DOS) for a 2D microsystem of non-interacting, indistinguishable bosons in an isotropic harmonic oscillator potential.

Overview

The problem of calculating the density of states is fundamental in statistical mechanics. For a quantum system, the density of states $g(E)$ is the number of distinct quantum states at a particular energy $E$.

This project implements a "decently fast" algorithm using dynamic programming to find the exact DOS. The energy levels of a single particle in a 2D quantum harmonic oscillator are given by $E_{n_x, n_y} = (n_x + n_y + 1)\hbar\omega$. We work in units of $\hbar\omega$ and define an "energy quantum number" $N = n_x + n_y$. The degeneracy of a single-particle energy level $N$ is $g_1(N) = N + 1$.

For a system of $P$ particles, the total energy quantum number is $N_{total} = \sum_{i=1}^{P} N_i$. This tool calculates the total degeneracy $g(P, N_{total})$ for all energy levels up to a specified maximum.

While the algorithm is optimized, the underlying problem is combinatorial and scales exponentially. Calculations for systems with more than ~36 particles can become time-consuming.