Raising and lowering operators

[intervoxel]

I'm confused about these two forms of the raising/lowering operators for the harmonic oscillator.
When each one is used?

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

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

 

[ansgar]

what?

 

[intervoxel]

what?

Oops! I had pushed the submit button before ending the post. Now it is corrected.

 

[ansgar]

it depends if you use bra-ket or "function" notation for your physics.