# Rate of change of a normalised wave function

I'm reading Weinberg's Lectures on QM. On top of p23 it says $$i\hbar\frac{d}{dt}\int|\psi(x,t)|^2d^3x=i\hbar\int\psi^*(x,t)\frac{\partial}{\partial t}\psi(x)d^3x-i\hbar\int\left(\frac{\partial}{\partial t}\psi^*(x,t)\right)\psi(x)d^3x.$$

I'm confused about why the second term has a minus sign and why $\psi=\psi(x)$ only.

• Comments to the question (v1): 1. There is no minus sign in the second term in Weinberg's 2013 book uploaded to Google books. 2. $\psi(x)$ instead of $\psi(x,t)$ is a typo. – Qmechanic Sep 1 '14 at 20:57
• I agree. It's just strange that Weinberg makes such mistakes... – LorentzNoether Sep 1 '14 at 21:10
• Related meta post: meta.physics.stackexchange.com/q/6111/2451 – Qmechanic Sep 2 '14 at 14:07
• Didn't know that there's a new edition!... Apparently mine is dated 2013 as well. – LorentzNoether Sep 2 '14 at 21:45