Barrier Decay Constant Calculator
The modified wave number k' is the barrier decay constant in the forbidden region.
Formula first
Overview
A larger barrier height or a smaller particle energy makes the decay constant larger, so the wave dies off faster.
Symbols
Variables
k' = k'
Apply it well
When To Use
When to use: Use this when the wavefunction must be matched across a finite barrier or finite well.
Why it matters: The tunneling picture explains why wavefunctions oscillate in allowed regions and decay exponentially in forbidden regions.
Avoid these traps
Common Mistakes
- Using an oscillatory solution where the energy is below the barrier.
- Forgetting to match both the wavefunction and its derivative at the boundaries.
- Underestimating how quickly the tunneling signal drops with barrier width.
- Interpreting k' as if it were a propagating-wave momentum.
One free problem
Practice Problem
How does the magnitude of the barrier decay constant k' change as the particle energy E approaches the barrier height V?
Solve for: k'
Hint: Look at the term (V-E) inside the square root.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Engineering LibreTexts, finite square well and tunneling-barrier notes, accessed 2026-04-09
- Peverati, The Live Textbook of Physical Chemistry 2, quantum weirdness/tunneling section, accessed 2026-04-09
- Engineering LibreTexts, field enhanced emission and tunnelling effects, accessed 2026-04-09
- NIST CODATA
- IUPAC Gold Book
- Griffiths, David J. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
- Wikipedia: Quantum tunneling
- Liboff, Richard L. (2003). Introductory Quantum Mechanics (4th ed.). Addison-Wesley.