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Wave function
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===Quantum harmonic oscillator=== The wave functions for the [[quantum harmonic oscillator]] can be expressed in terms of [[Hermite polynomial]]s {{math|''H<sub>n</sub>''}}, they are <math display="block"> \Psi_n(x) = \sqrt{\frac{1}{2^n\,n!}} \cdot \left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \cdot e^{ - \frac{m\omega x^2}{2 \hbar}} \cdot H_n{\left(\sqrt{\frac{m\omega}{\hbar}} x \right)} </math> where {{math|1=''n'' = 0, 1, 2, ...}}. [[File:Hydrogen Density Plots.png|thumb|upright=1.5|The electron probability density for the first few [[hydrogen atom]] electron [[atomic orbital|orbitals]] shown as cross-sections. These orbitals form an [[orthonormal basis]] for the wave function of the electron. Different orbitals are depicted with different scale.]]
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