Free Quantum Tunneling Probability Calculator
Estimate the transmission coefficient for a rectangular barrier: T = exp(-2 * d * sqrt(2m(V-E)) / hbar).
eV
eV
m
kg
Transmission Coefficient
0.2348281293
Transmission Coefficient vs Barrier Height (V)
Quantum Tunneling
In quantum mechanics, a particle can pass through a potential barrier even if its energy is below the barrier height.
Approximate Transmission
T = exp(-2d sqrt(2m(V-E)) / hbar)
The probability drops exponentially with barrier width and the square root of the energy deficit.
Example Calculation
Electron (m = 9.109e-31 kg) with E = 3 eV hitting a 5 eV barrier, 1 angstrom wide.
- 01V - E = 2 eV = 2 * 1.602e-19 = 3.204e-19 J
- 02sqrt(2m(V-E)) = sqrt(2 * 9.109e-31 * 3.204e-19) = sqrt(5.837e-49) = 7.640e-25
- 03Exponent = -2 * 1e-10 * 7.640e-25 / 1.0546e-34 = -1.449
- 04T = exp(-1.449) = 0.235
Frequently Asked Questions
Learn More
Understanding Newton's Laws of Motion
A comprehensive guide to Newton's three laws of motion. Learn about inertia, force and acceleration, action-reaction pairs, and how these principles govern everyday physics.