Harmonic Oscillator Ladder Operators - What is (ahat_+)^+?

[gabriellelee]

Homework Statement

What is (ahat_+)^+?

Relevant Equations

Please see below for the question.

I know that ahat_+ = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)+i(phat)) and ahat_- = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)-i(phat)). But I'm not sure what (ahat_+)^+ could be.

 

[PeroK]

I think that is $\hat a_+^{\dagger} = \hat a_-$, where $^{\dagger}$ represents the Hermitian conjugate of an operator.