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limddavid
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Homework Statement
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.
Homework Equations
Groups?
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?