Particle in a Box Energy Levels
Quantized energy levels for a particle confined to a one-dimensional infinite potential well.
Variables
Derivation
Solved from Schrödinger equation with boundary conditions ψ(0) = ψ(L) = 0.
Your notes
Constants in this formula
Check value
Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- n = 2 (Quantum number (n = 1, 2, 3...))
- h = 6.626 070 15 × 10⁻³⁴ J·s (Planck constant)
- m = 3 kg (Particle mass)
- L = 4 m (Box length)
Result: En = 4.573417 × 10⁻⁶⁹ J
Other modern physics formulas with the same quantities
- Photon Energy (Planck) (Quantum Mechanics) shares Planck constant
- Photoelectric Effect (Quantum Mechanics) shares Planck constant
- Stopping Potential (Quantum Mechanics) shares Planck constant
- de Broglie Wavelength (Quantum Mechanics) shares Planck constant
- Compton Scattering (Quantum Mechanics) shares Planck constant
- Photon Momentum (Quantum Mechanics) shares Planck constant
Where this formula is listed
- Modern Physics formulas, under Quantum Mechanics, alongside Heisenberg Uncertainty Principle, Energy-Time Uncertainty, Fermi Energy, Photoelectric Threshold Frequency and Bragg's Law.
- In the modern physics list it comes after Time-Dependent Schrödinger Equation and before Compton Scattering.
- Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Particle in a Box Energy Levels formula?
Particle in a Box Energy Levels is written E_n = n²h²/(8mL²). Quantized energy levels for a particle confined to a one-dimensional infinite potential well. It belongs to Modern Physics, under Quantum Mechanics.
What are the units in E_n = n²h²/(8mL²)?
In SI units, E_n is energy of level n, measured in J; n is quantum number (n = 1, 2, 3...) (dimensionless); h is planck constant, measured in J·s; m is particle mass, measured in kg; L is box length, measured in m.
How is the Particle in a Box Energy Levels formula derived?
Solved from Schrödinger equation with boundary conditions ψ(0) = ψ(L) = 0. The result is E_n = n²h²/(8mL²).