I'm confused about these two forms of the raising/lowering operators for the harmonic oscillator.(adsbygoogle = window.adsbygoogle || []).push({});

When each one is used?

[tex]

a_+\psi_n=i\sqrt{(n+1)\hbar\omega} \psi_{n+1}

[/tex]

[tex]

a_-\psi_n=-i\sqrt{n\hbar\omega} \psi_{n-1}

[/tex]

[tex]

a_+|\psi_n\rangle=\sqrt{n+1} |\psi_{n+1}\rangle

[/tex]

[tex]

a_-|\psi_n\rangle=\sqrt{n} |\psi_{n-1}\rangle

[/tex]

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# Raising and lowering operators

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