(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A translation operator T(a) coverts ψ(x) to ψ(x+a),

T(a)ψ(x) = ψ(x+a)

In terms of the (quantum mechanical) linear momentum operator p_x = -id/dx, show that T(a) = exp(iap_x), that is, p_x is the generator of translations. Hint. Expand ψ(x+a) as a Taylor series.

2. Relevant equations

Groups?

3. The attempt at a solution

I'm lost at the hint. To expand ψ(x+a) as a Taylor series, don't I need a point around which to expand it?

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# Taylor Series/Groups

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