Hydrogen |ψ|² (xz slice)
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.
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