Quantum Tunneling Calculator (Rectangular Barrier)
Exact and approximate transmission probability of a particle through a rectangular potential barrier.
How to use the Quantum Tunneling Calculator
- Enter or select: Particle, Particle energy E, Barrier height V₀, Barrier width a.
- Fill in what you know of: Custom mass — leave the unknown empty.
- The results (Decay constant κ, Transmission T (exact), Approximation e^(−2κa), Reflection R = 1 − T, Penetration depth 1/κ) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- κ = √(2m(V₀ − E))/ħ
- T = [1 + V₀² sinh²(κa) / (4E(V₀ − E))]⁻¹
- T ≈ e^(−2κa) (κa ≫ 1)