Finite Square Well Potential Calculator
This is the standard finite potential profile used for a finite square well or barrier.
Formula first
Overview
The potential is zero inside the active region and finite outside, which is the simplest model that still produces tunneling and bound states.
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.
- Assuming an infinite wall when the model is explicitly finite.
One free problem
Practice Problem
In the region (0, L), what is the general form of the wavefunction if the total energy E is greater than zero but less than V?
Solve for: $V(x)
Hint: Consider the sign of (E - V) inside the well where the potential is zero.
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
- Griffiths, D. J. (2018). Introduction to Quantum Mechanics.
- Liboff, R. L. (2002). Introductory Quantum Mechanics.
- Griffiths, David J. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
- Landau, L. D., & Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory (Vol. 3, 3rd ed.). Pergamon Press.
- NIST CODATA Value of the Planck constant