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1D_harmonic_oscillator.py
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1D_harmonic_oscillator.py
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import numpy as np
from qmsolve import Hamiltonian, SingleParticle, init_visualization, Å, eV
#=========================================================================================================#
#We define the Hamiltonian of a single particle confined in an harmonic oscillator potential.
#Then, we compute its eigenstates.
#=========================================================================================================#
#interaction potential
def harmonic_oscillator(particle):
k = 100 * eV / Å**2
return 0.5 * k * particle.x**2
#define the Hamiltonian
H = Hamiltonian(particles = SingleParticle(),
potential = harmonic_oscillator,
spatial_ndim = 1, N = 512, extent = 20*Å)
#Diagonalize the Hamiltonian and compute the eigenstates
eigenstates = H.solve(max_states = 30)
print(eigenstates.energies) # the printed energies are expressed in eV
# Visualize the Eigenstates
visualization = init_visualization(eigenstates)
visualization.slider_plot() #interactive slider
# (Optional: Visualize a specific eigenstate)
# visualization.plot_eigenstate(0)