- #1
jror
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Homework Statement
Given the wave function of a particle [itex] \Psi(x,0) = \left(\frac{2b}{\pi}\right)^{1/4}e^{-bx^2} [/itex], what is the probability of finding the particle between 0 and [itex] \Delta x [/itex], where [itex] \Delta x [/itex] can be assumed to be infinitesimal.
Homework Equations
The Attempt at a Solution
I proceed as I normally would when trying to obtain the probability of finding a particle within a certain interval, by calculating the integral ##\int_a^b |\Psi(x,0)|^2 dx##, where the limits here are ##a=0## and ##b=\Delta x##. I am stuck in trying to calculate the Gaussian with these limits. I know the answer in the infinite limit, but for abritrary limits one usually has to deal with error functions. What is the trick here with setting the upper limit to some assumed infinitesimal number? Would appreciate a hint!