Particle in an infinite well
An electron shut in a box can only have certain energies.
A particle confined to a one-dimensional well of width L must have a wave function that vanishes at the walls, so it can only be a standing wave, and its energy is quantized: Eₙ ∝ n²/L². The probability density |ψₙ|² of a stationary state does not change with time and has n − 1 nodes; a superposition of two stationary states "sloshes" back and forth in the well at frequency ΔE/h, which is how a quantum state evolves in time.
Probability density |Ψ|²
A stationary state's probability density doesn't change with time; it has n − 1 nodes.
Think about it
What happens to the ground-state energy if you halve the width of the well?
It becomes 4 times as large. Eₙ is inversely proportional to L², so the narrower the well, the higher the energy — which is also why the color of quantum dots changes with their size.
Model assumptionsParticle is an electron · infinitely deep well · superposition oscillation slowed to once every 3 s on screen
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.