I'm reading through the book Quantum Mechanics (Second Edition) by David J. Griffiths and it got to the part about proving that if you normalise a wave function, it stays normalised (Page 13).(adsbygoogle = window.adsbygoogle || []).push({});

That part that I don't get is how they say:

## \dfrac{i \hbar}{2m} \left( \Psi^* \dfrac{\partial^2 \Psi}{\partial x^2} - \dfrac{\partial^2 \Psi^*}{\partial x^2} \Psi \right) = \dfrac{\partial}{\partial x} \left[\dfrac{i \hbar}{2m} \left( \Psi^* \dfrac{\partial \Psi}{\partial x} - \dfrac{\partial \Psi^*}{\partial x} \Psi \right) \right] ##

How can they just pull out a partial operator like that?

Because if you expand it out again it would give you:

## \dfrac{i \hbar}{2m} \left( \dfrac{\partial}{\partial x} \left[ \Psi^* \dfrac{\partial \Psi}{\partial x}\right] - \dfrac{\partial}{\partial x} \left[ \dfrac{\partial \Psi^*}{\partial x} \Psi \right] \right) ##

The operator will be applied to the wrong ## \Psi ## and also won't you need to apply the product rule to is as well?

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# Pulling out partial derivatives?

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