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Home/Chemistry/Landau Levels in a Magnetic Field

Landau Levels in a Magnetic Field

This interactive simulator explores Landau Levels in a Magnetic Field in Chemistry. Charged particle in a uniform B-field: equally-spaced Landau ladder E_n = ℏω_c(n+½) with cyclotron frequency ω_c = qB/m, magnetic length ℓ_B = √(ℏ/qB) and orbit radius r_n = ℓ_B√(2n+1). Animated cyclotron orbit + linear-in-B fan diagram; the n_B = qB/h degeneracy underlies the quantum Hall effect. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Chemistry.

Key terms

  • landau
  • levels
  • magnetic
  • field
  • landau levels
  • chemistry

Charge in uniform B

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Two-dimensional charged particle in a uniform perpendicular magnetic field B. Quantization gives the equally-spaced Landau ladder E_n = ℏω_c(n+½) with cyclotron frequency ω_c = qB/m and magnetic length ℓ_B = √(ℏ/qB). Each level is enormously degenerate, with n_B = qB/h states per unit area — the basic ingredient of the integer quantum Hall effect. Units: ℏ = q = m = 1.

Measured values

ω_c = qB/m1.000
ℓ_B = √(ℏ/qB)1.000
r_n = ℓ_B√(2n+1)2.236
E_n = ℏω_c(n+½)2.500

How it works

Landau levels of a 2-D charged particle in a perpendicular magnetic field B: the equally-spaced ladder E_n = ℏω_c(n+½), the magnetic length ℓ_B = √(ℏ/qB), the cyclotron radius r_n, and the linear-in-B fan diagram — the building block of the integer quantum Hall effect.