A particle moving in one dimension (the -axis) is described by the wave function

Question

A particle moving in one dimension (the -axis) is described by the wave function psi(x) where = 2.00, > 0, and the -axis points toward the right. psi(x) = { A*exp(-bx), for x >= 0 A*exp(bx), for x < 0 b = 2.00 m^-1 A = 1.41 m^1/2 part 1 Find the probability of finding this particle in each of the following regions: within 55.0cm of the origin. part 2 Find the probability of finding this particle in each of the following regions: between x=0.450m and x=1.05m . I have already plugged x i to the function giving 2*1.41*exp(-2*0.55) = 93.8% but it is not correct my friend found the answer to his which was wanting to know the probability for 60.0cm. everything else was the same and the percent was 90.9%. i dont know how this percent was found?

Explanation / Answer

P = 2 * ??^2 dx integration from x=0 to x=0.55 P = 2 * ?(1.41*e^(-2x))^2 dx P = 2 * ?(1.41)^2 * e^(-4x)) dx P = 2 * 1.41*1.41 * (e^(-4x)/(-4)) P = 2 * 1.41*1.41 * ( (e^(-4*0.55)/(-4)) - (e^(-4*0.55)/(-4)) ) P = 2 * 1.41*1.41 * ( (0.1108031/(-4)) - (1/(-4)) ) P = 0.884 P = 88.4 %

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