Modern Physics
Particle in a Box Energy Levels
Quantized energy levels for a particle confined to a one-dimensional infinite potential well.
Variables
E_nJ
Energy of level n
nunitless
Quantum number (n = 1, 2, 3...)
hJ·s
Planck constant
mkg
Particle mass
Lm
Box length
Derivation
Solved from Schrödinger equation with boundary conditions ψ(0) = ψ(L) = 0.
Your notes
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Common questions
What is the Particle in a Box Energy Levels formula?
Particle in a Box Energy Levels is written Eₙ = n² h²/8mL². 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 Eₙ = n² h²/8mL²?
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 Eₙ = n² h²/8mL².