English: Computed 3s₀ orbital of an electron's eigenstate of the energy- and angular momentum operators in the Coulomb-field of a hydrogen nucleus. Such an eigenstate keeps its spatial shape over time while obeying the Schrödinger equation and only advances its complex phase.

The wavefunction is:

${\displaystyle \psi _{3,0,0}(r,\vartheta ,\varphi )={\sqrt {{\left({\frac {2}{3\,a_{0}}}\right)}^{3}{\frac {1}{18}}}}\cdot e^{\textstyle -r/(3\,a_{0})}\cdot L_{2}^{1}(2\,r/(3\,a_{0}))\cdot {\frac {1}{\sqrt {4\,\pi }}}}$

The state is an eigenstate of H, L² and L_z, which constitute a complete set of commuting observables.
The quantum numbers mean that the following quantities have a sharp certain value:

• n = 3: Energy: ${\displaystyle E=-1\,\mathrm {Ry} /n^{2}=-13.6\,\mathrm {eV} /9}$
• l = 0: Angular momentum: ${\displaystyle |L|={\sqrt {l\,(l+1)}}\,\hbar =0}$
• m = 0: Angular momentum in z-direction: ${\displaystyle L_{z}=m\,\hbar =0}$

Since l=0, this is called a s-orbital.
The depicted rigid body is where the probability density exceeds a certain value. The color shows the complex phase of the wavefunction, where blue means real positive, red means imaginary positive, yellow means real negative and green means imaginary negative. The image is raytraced using modified Phong lighting.

Half of the orbital was cut away to make the internal structure visible.