- #1

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[tex] \frac {d} {dt} \int_{-\infty}^{\infty}|\Psi(x,t)|^2 dx = \int_{-\infty}^{\infty} \frac{\partial}{\partial t} |\Psi(x,t)|^2 dx [/tex]

In the next line, he gives the following explanation:

"Note that the integral is a function of only t, so I use the total derivative (d/dt) in the first term, but the integrand is a function of x as well as t, so it's a partial derivative ([tex]\frac{\partial}{\partial t}[/tex]) in the second one."

It is this explanation that I am having difficulty understanding. I just don't understand why he replaced the total derivative with a partial derivative, despite his explanation. Could someone please explain what he is trying to explain in greater detail? Thanks.