If a quantum particle hits a rectangular potential barrier, then both the transmission coefficient

and the reflection coefficient

are periodic functions of the potential width

in the case

, but

and

are decreasing and increasing functions, respectively, in the case

. Furthermore,

and

depend on the quotient

of the wavenumbers

of the incident particle and

of the wave inside the barrier;

. This is shown interactively. The behavior of a quantum particle contrasts with that of a classical particle, where

,

, or vice versa. The "quantum tunneling" effect is a pure quantum effect in the case

. The formulas for

and

follow by solving the time-independent wave equation (Schrödingers equation) with boundary conditions.