Transmission Coefficient
Calculate quantum transmission probability through a square potential barrier for particle energy and barrier height.
Quantum Transmission Through a Barrier
When a particle encounters a square potential barrier, quantum mechanics allows partial transmission even when the particle energy is below the barrier height. This tunneling effect is central to scanning tunneling microscopy, alpha decay, and semiconductor devices.
Transmission Approximation
$$T = \frac{4 E (V_0 - E)}{V_0^2} \quad \text{for } E < V_0$$For sub-barrier energies \(E\), this approximation gives the transmission coefficient \(T\) as a fraction of incident particles that pass through. When \(E > V_0\), classical transmission applies and \(T = 1\) in this simplified model. Reflection coefficient is \(R = 1 - T\).
Barrier Width
Barrier width in nanometers affects tunneling probability in full quantum models (exponential decay inside the barrier). This calculator uses the energy-only approximation; width is recorded for reference when comparing scenarios.
Related tools: Harmonic Wave Equation Calculator and Floating Point Calculator.
Frequently Asked Questions
What is the transmission coefficient?
The transmission coefficient \(T\) is the probability that a particle passes through a potential barrier. It ranges from 0 (fully reflected) to 1 (fully transmitted).
When does tunneling occur?
Tunneling dominates when particle energy \(E\) is less than barrier height \(V_0\). The particle has a nonzero chance to appear on the far side despite insufficient classical energy.
Why is T = 1 when E exceeds V0?
In this simplified model, particles with energy above the barrier classically pass over it with full transmission. More detailed models include interference and partial reflection above the barrier.
What units are used for energy?
Barrier height and particle energy are entered in electron volts (eV), standard for atomic and solid-state physics.
How does barrier width affect tunneling?
Wider barriers exponentially suppress tunneling in full quantum treatments. The approximation here ignores width; use it for quick energy comparisons only.
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