Calculadora de Probabilidad de Túnel Cuántico — Fórmula

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.

    Ejemplo Resuelto

    Electron (m = 9.109e-31 kg) with E = 3 eV hitting a 5 eV barrier, 1 angstrom wide.

    1. V - E = 2 eV = 2 * 1.602e-19 = 3.204e-19 J
    2. sqrt(2m(V-E)) = sqrt(2 * 9.109e-31 * 3.204e-19) = sqrt(5.837e-49) = 7.640e-25
    3. Exponent = -2 * 1e-10 * 7.640e-25 / 1.0546e-34 = -1.449
    4. T = exp(-1.449) = 0.235