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Home/Chemistry/Hydrogen |ψ|² (xz slice)

Hydrogen |ψ|² (xz slice)

Coulomb hydrogen Z=1: |R_nl|² × |Y_lm|² colormap in the xz plane for textbook n,l states.

Hydrogen |ψ|² (xz)

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Real Coulomb hydrogen (Z=1) radial factors R_nl(r) in a₀ units; angular factor is |Y_lm|² averaged over φ so the xz map is representative for m≠0.

Measured values

State2p_z

About this model

Hydrogen-like Coulomb eigenstates ψ_{nlm}(r, θ, φ) = R_nl(r) Y_lm(θ, φ) in atomic units (a₀, Z = 1). The simulator evaluates |ψ|² on an xz grid using textbook radial factors R_nl(r) and the standard spherical-harmonic angular density |Y_lm|², which for complex Y_lm depends only on θ for the squared magnitude. The result is a false-color map of where the electron is likely to be found in that plane for common n, l combinations.

Who it's for: Physical chemistry and quantum mechanics courses connecting quantum numbers to spatial images.

Key terms

  • Hydrogen Atom
  • Radial Wavefunction
  • Spherical Harmonics
  • Probability Density

How it works

Probability density |ψ_{nlm}|² in the xz plane for hydrogen-like Z=1 eigenstates: analytic R_nl(r) with standard spherical-harmonic angular factors (pedagogical colormap).

Frequently asked questions

How does this differ from the “Orbital Shapes (Schematic)” page?
That page emphasizes angular patterns with a phenomenological radial envelope. Here R_nl(r) follows the hydrogenic Coulomb formulas in atomic units, so radial nodes for n > l + 1 appear in the map.