Retrieving "Energy Eigenstates" from the archives

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1. Harmonic Oscillator

   Linked via "energy eigenstates"

   Creation and Annihilation Operators
   The QHO is canonically solved using the algebraic method employing ladder operators (creation, $\hat{a}^\dagger$, and annihilation, $\hat{a}$, operators). These operators act on the energy eigenstates $|\psi_n\rangle$:
   $$\hat{a}|\psin\rangle = \sqrt{n}|\psi{n-1}\rangle$$