When solving the quantum harmonic oscillator often ladder operators (that send energy eigenstates to higher or lower energy eigenstates) are introduced that allow one to algebraically solve the system. Similarly (but with much more difficulty) such operators can be introduced to solve the non-relativistic Hydrogen atom.(adsbygoogle = window.adsbygoogle || []).push({});

I was wondering for what systems can these ladder-type operators be found, and for such systems is there a canonical method of finding them? (So for example do such operators exist for the infinite square well or the Dirac Hydrogen atom?)

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# Algebraic (ladder) solutions in QM

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