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I was given this problem: Let the state $f(x)=e^{-|x|}$ and an operator $P=-i\frac{d}{dx}$.

(a) What is the probability that a measure of P results in the interval $[0,1]$

(b) What is the Fourier Transform of $f(x)$.

Question: Why is (a) asked before (b), wouldn't we need to use the result from (b) to compute (a)?

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Could you define "measurement of $P$" for the non-initiated ? –  Sasha Dec 2 '11 at 20:47
oh...this is actually quantum mechanics, f(x) is a state of a physical system, and P is some property of the state (i.e position, momentum etc). The measurement returns a number. And we are trying to find the probability that the number will be between 0 and 1. –  Xiaowen Li Mar 10 '12 at 8:44
If it's quantum mechanics, shouldn't it be $f(x)=e^{-\color{red}{\bf i}|x|}$? –  draks ... Jul 19 '12 at 19:57

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