Weird factoring out of a derivative

Question

Is it possible to just factor out the derivative like this:

$$ x \left[ \frac{d^2 \Psi}{d x^2} \cdot \Psi^* - \frac{d^2 \Psi^*}{d x^2} \cdot \Psi \right] = x \, \frac{d}{dx} \left( \frac{d \Psi}{d x} \cdot \Psi^* - \frac{d \Psi^*}{d x} \cdot \Psi \right) $$

$\Psi$ is just some function of $x$ while $\Psi^*$ is its complex conjugate. I am in doubts as we have products inside square brackets...

score 2 · Accepted Answer · answered Mar 20 '13 at 12:10

2

HINT. Try to go from the other side: compute the derivative
$$\frac{d}{dx} \left( \frac{d \Psi}{d x} \cdot \Psi^* - \frac{d \Psi^*}{d x} \cdot \Psi \right)$$ using the product rule and see what happens.

answered Mar 20 '13 at 12:10

gev

594

Thank you for the hint! Was a good one! This equality is TRUE! – 71GA Mar 20 '13 at 12:16

Weird factoring out of a derivative

1 Answers1