Quantum Tunneling Probability Calculator — Formula
## 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.
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.
Esempio Risolto
Electron (m = 9.109e-31 kg) with E = 3 eV hitting a 5 eV barrier, 1 angstrom wide.
- V - E = 2 eV = 2 * 1.602e-19 = 3.204e-19 J
- sqrt(2m(V-E)) = sqrt(2 * 9.109e-31 * 3.204e-19) = sqrt(5.837e-49) = 7.640e-25
- Exponent = -2 * 1e-10 * 7.640e-25 / 1.0546e-34 = -1.449
- T = exp(-1.449) = 0.235