Quantum Tunneling Calculator

Particles can pass through classically forbidden barriers. In LFM, this emerges from wave propagation — the wavefunction doesn't abruptly stop at the barrier.

🌟 Tunneling Powers Our World

☀️ Nuclear Fusion

Protons tunnel through Coulomb barrier to fuse in stars — without tunneling, the Sun wouldn't shine!

🔬 STM Imaging

Electrons tunnel between tip and surface, enabling atomic-resolution microscopy (Nobel 1986)

💾 Flash Memory

Data stored by tunneling electrons onto floating gates — your USB drive is quantum!

LFM Mechanism

In LFM, the barrier represents a region with elevated effective χ. The particle wavefunction (ψ) decays exponentially inside the barrier (evanescent wave), but for finite barriers, a non-zero amplitude emerges on the other side.

Decay constant:
κ = √(2m(V₀-E)) / ℏ
Transmission (thick barrier):
T ≈ exp(−2κL)

Select Scenario

Tunneling Analysis

Transmission Probability
T = 3.6e-7
Quantum tunneling through 2.50 eV barrier
Decay Length
0.123 nm
1/κ
Barrier Regime
Thick
2κL = 16.20
Reflection ProbabilityR = 100.00%
de Broglie Wavelengthλ = 0.8672 nm
Exponential Approx.exp(−2κL) = 9.2e-8
vs Thermal (300K)3.62e+35×
χ_barrier/χ₀ (LFM)1.000009

Wavefunction Through Barrier

IncidentV₀Transmitted
|ψ|² = 1
|ψ|² = 3.6e-7

The wavefunction decays exponentially inside the barrier but maintains non-zero amplitude. Decay factor: exp(−16.2)

Quantum tunneling theory developed by Gamow, Gurney, and Condon (1928) to explain alpha decay.
LFM describes tunneling as wavefunction penetration through χ-elevated regions.