Poço infinito Eₙ
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
This calculator determines quantized energy levels for a particle in an infinite potential well, a fundamental concept in quantum mechanics. The formula Eₙ = n²π²ℏ²/(2mL²) calculates energy using the quantum number n, reduced Planck constant ℏ, particle mass m, and well width L. It's used in systems like electrons in nanostructures or theoretical models.
The formula reflects energy quantization due to the particle's wave nature. For n = 1, 2, 3..., each value represents a stationary state. Energy scales with n², showing higher states require more energy. The model assumes the particle cannot escape (infinite potential at edges).
Apply this calculator to physical problems involving one-dimensional confinement, such as nanotechnology simulations or spectroscopy. Ensure units: ℏ in J·s or eV·s, L in meters. Avoid confusing with finite wells, where the formula changes due to tunneling probability.
Frequently asked questions
What does the quantum number n represent?
The quantum number n indicates the particle's energy level, an integer (n ≥ 1) defining the stationary state.
How does the well width (L) affect energy?
Smaller L increases energy as the particle is more confined. Energy is inversely proportional to L².
Can this calculator be used for particles other than electrons?
Yes, as long as you know the particle's mass. The formula applies to any particle with a defined mass.
Why is the well called 'infinite'?
Because the potential at edges is infinitely high, preventing the particle from escaping.
What units should I use for ℏ?
Use joule-seconds (J·s) or electronvolt-seconds (eV·s), common in quantum physics.