I am following Griffiths' intro to quantum mechanics and struggling(already) on page 16. When a particle is in state ##\Psi##,(adsbygoogle = window.adsbygoogle || []).push({});

$$\frac{d<x>}{dt} = \frac{i\hbar}{2m}\int_{-\infty}^{\infty} x\frac{\partial}{\partial t}\bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial x}\Psi\bigg )dx$$

By integration-by-parts, this becomes

$$\frac{i\hbar}{2m}\bigg [x\bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial x}\Psi \bigg)-\int_{-\infty}^{\infty} \bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial x}\Psi\bigg )dx\bigg ]$$

But the author throws the first term away by reasoning "##\Psi## goes to zero at (##\pm\infty##)"

but as at infinity, x also goes to infinity, so the first term is infinity x 0, which is not clear to me if the whole term could be thrown away. Can someone please explain this?

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# About the expectation value of position of a particle

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