At a certain instant of time, a one-particle, one - dimensional system has = (2/b3)1/2xe-|x|/b, where

Question:

At a certain instant of time, a one-particle, one - dimensional system has Ψ = (2/b3)1/2xe-|x|/b, where b = 3.000 nm. If a measurement of x is made at this time in the system, find the probability that the result
(a) Lies between 0.9000 nm and 0.9001 nm (treat this interval as infinitesimal);
(b) Lies between 0 and 2 nm (use the table of integrals in the Appendix, if necessary).
(c) For what value of x is the probability density a minimum? (There is no need to use calculus to answer this.)
(d) Verify that Ψ is normalized.