# Transmission and Reflection Coefficients of Quantum Particles

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This Demonstration shows the transmission coefficient and the reflection coefficient of a quantum particle with energy hitting a rectangular potential barrier. See how the height of the potential barrier affects and by comparing the cases and . The dimensionless coordinate is the product of the wavenumber for the wave inside the barrier and the barrier width .

Contributed by: Reinhard Tiebel (March 2011)

Open content licensed under CC BY-NC-SA

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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.

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