Inspired by the previous problem, find the generators that rotate the momentum vector (mathbf{p}) about the (x,

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Inspired by the previous problem, find the generators that rotate the momentum vector \(\mathbf{p}\) about the \(x, y\), and \(z\) axes by infinitesimal angles.

Data from previous problem

Using Eq. (11.140), show that if we use G= ϵLx as a generator of a transformation (where \(L_{x}\) is the \(x\)-component of the angular momentum), we end up rotating the components of the position vector \(\mathbf{r}\) by an infinitesimal angle \(\epsilon\) about the \(x\)-axis. Show this by applying the generator onto an arbitrary function of position \(A(\mathbf{r})\). Similarly, find the generators that rotate the position vector about the \(y\) and \(z\)-axes.

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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