natalidesanti / harmonic_oscillator

This repo contains some codes to work with quantum and classical harmonic oscillator

Harmonic Oscillator

This repo contains some codes to work with quantum and classical harmonic oscillator. Folders contain the main results and the programs are in the scope of the repo.

Code descriptions

• analytical.f: computes the probability of finding a particle for the classical harmonic oscillator (analitically), together with the density probability of the quantum harmonic oscillator in order to compare each order and test the Correspondence Principle;
• plot-analytical.py: plots the comparison: classical probability X quantum density of probability, using analytical results. Besides, this program moves the data files created in the main directory by analytical.f to the folder analytical/
• energies.f: computes eigenvalues for the energy of the quantum harmonic oscillator using Numerov's method;
• hermite.f: computes the Hermite polynomials until order 5;
• plot_hermite.py: plots the Hermite polynomials until order 5. Besides, this program moves the data files created in the main directory by hermite.f to the folder hermite/;
• numerov.f: computes the probability density for the quantum harmonic oscillator using Numerov's method; in order to prove the Correspondence Principle;
• plot-numerov.py: plots the comparison Numerov's X analytical probability densities. Besides, this program moves the data files created in the main directory by numerov.f to the folder numerov/;

An interesting explanation about the theory and plots of this repo is available in my blog: natalidesanti.