= Energy level
{title2=$E_n$}
{wiki}
An energy level is an allowed <energy eigenvalue> of a <Quantum Hamiltonian>. Its corresponding <energy eigenstates> satisfy $H|n\rangle=E_n|n\rangle$. Several independent <energy eigenstates> may share one energy level; their number is the <energy-level degeneracy>. A <quantum superposition> of different <energy eigenstates> need not have a definite <energy>, even though an ideal <energy measurement> yields one of the allowed outcomes.
<Quantum confinement> often produces discrete energy levels: the <quantum harmonic oscillator> has $E_n=\hbar\omega(n+1/2)$. An unconfined <free particle> instead has a <continuous spectrum>. In <spectroscopy>, a transition between two energy levels exchanges approximately $|E_f-E_i|=h\nu$ with a <photon>; recoil and external fields can affect the measured <frequency>. <Selection rules> determine which energy differences produce observable <spectral lines>.
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