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.

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.

Other simulators in this category — or see all 62.

View category →

NewSchool

Hydrogen: Balmer / Lyman Lines

Rydberg wavelengths 1/λ = R_H (1/n_f² − 1/n_i²); Lyman, Balmer, and Paschen series on a linear spectrum strip.

Launch Simulator

NewUniversity / research

Heisenberg Product σ_x σ_p

Gaussian position and momentum widths with ℏ = 1; momentum “excess” over the minimum-uncertainty floor.

Launch Simulator

NewUniversity / research

β⁻ Decay: Electron Spectrum

Continuous kinetic-energy spectrum up to endpoint Q (allowed-decay phase space); missing energy carried by the antineutrino.

Launch Simulator

NewSchool

Nernst Equation

E = E° − (RT/nF) ln Q: sliders for E°, n, T, and reaction quotient.

Launch Simulator

NewSchool

Buffer Solution

Henderson–Hasselbalch vs strong acid: pH curve as H⁺ is added (mole model).

Launch Simulator

NewSchool

Acid Dissociation α(pH)

α = 1/(1+10^(pKa−pH)); half-equivalence at pH = pKa; curves for α and 1−α vs pH.

Launch Simulator

Hydrogen |ψ|² (xz slice)

How it works

Frequently asked questions

More from Chemistry

Hydrogen: Balmer / Lyman Lines

Heisenberg Product σ_x σ_p

β⁻ Decay: Electron Spectrum

Nernst Equation

Buffer Solution

Acid Dissociation α(pH)

Hydrogen |ψ|² (xz slice)

How it works

Frequently asked questions