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I'm not sure how they got equation 4.5

Starting from ##\psi'> = U_{(\vec{a})} |\psi>## where ##U_{(\vec{a})} = e^{\frac{-i\vec {a} \cdot \vec {p}}{\hbar}}##

Differentiating both sides with respect to ##a_x## and setting ##a = 0##:

[tex]\frac{\partial |\psi'>}{\partial a_x} = \frac{-ip_x}{\hbar} U_0 |\psi> + U_0\frac{\partial |\psi>}{\partial a_x} [/tex]

Using the fact that ##U_0 = 1##,

[tex]\frac{\partial |\psi'>}{\partial a_x} = \frac{-ip_x}{\hbar} |\psi> + \frac{\partial |\psi>}{\partial a_x} [/tex]

It's wildly different from what they have..

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# Translation of a ket

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