# Operation on Complex conjugate

Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?

• In part it's conventional. – ZeroTheHero Dec 6 '17 at 21:11

$$\int\psi^* \hat{F} \varphi = \int (\hat{F}^+ \psi)^* \varphi$$
also, if F is an Hermitian operator $$\int \Psi \hat{F} \Psi^* = \int \Psi^* \hat{F}\Psi$$
Take the kinetic energy operator and ground state wave function for a particle in a box with width of $L$ as an example (in 1D) $$\hat{T}=-\frac{\hbar}{2m}\frac{d}{dx^2}$$ and $$\psi=\sqrt{\frac{2}{L}}\sin\frac{\pi}{L}x$$ Obviously, $\hat{T}\psi$ means something and $\psi^{*}\hat{T}$ means something else.