042
Particle in a box
Standing waves between two walls, whose energies spread as 1 : 4 : 9.
Field
Detail
Study
042
Chapter
Quantum mechanics
Equation
ψₙ(x) = √(2/L) sin(nπx/L), Eₙ ∝ n²
What moves
n, the state number; L, the box width
Structure
Film
Colour means
energy
Posted
A wave is trapped between two walls and must be zero at both. Only whole numbers of half-waves fit, so only certain shapes are allowed. Seen from the side each is the flat textbook curve; as the camera turns, the wave is revealed turning about its axis, and the higher states turn faster. The energy of state n grows with n squared, which is why the levels on the ladder spread 1, 4, 9.