Quantum Particle in a Box
Visualize energy levels, wavefunctions, and probability densities for an electron in a one-dimensional infinite square well.
Free theory articleVisualize energy levels, wavefunctions, and probability densities for an electron in a one-dimensional infinite square well.
Concept & interpretation
An electron confined between impenetrable walls has discrete stationary states. Its spatial wavefunction can be positive or negative; probability density is its nonnegative squared magnitude. The normalized coordinate q = x/L runs from the left wall to the right wall.
Compare widths, nodes and probability
Open the Quantum Particle in a Box module and use its labeled text controls.
- Set Well width L to 1, Quantum number n to 1 and Probe fraction q to 0.5. Check the ground-state prediction above.
- Set Quantum number n to 2. The highlighted energy becomes 1.50412065071 eV and the central node appears in both curves.
- Set Quantum number n back to 1, Well width L to 2 and Probe fraction q to 0.25. Energy becomes 0.0940075406697 eV, signed amplitude is 1, physical density is 0.5/nm and left probability is approximately 0.0908450569081.
- Try Probe fraction q equal to 0 and then 1. Amplitude and density vanish at both walls; cumulative probability is respectively zero and one.
- Drag the plots to pan and use Reset view to restore their framing. This keeps the entered physical parameters.