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)
Formule
## 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)** - *V* = barrier height (eV, converted to J) - *E* = particle kinetic energy - *d* = barrier width - *m* = particle mass - *hbar* = reduced Planck constant The probability drops exponentially with barrier width and the square root of the energy deficit.
Exemple Résolu
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