- #1

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[tex] \Psi(x,0) = \left\{ \begin{array}{ccc}

A\frac{x}{a}, & if 0 \leq x \leq a, \\

A\frac{b-x}{b-a}, & if a \leq x \leq b, \\

0, & otherwise,

\end{array} \right

[/tex]

where A, a, and b are constants.

(a) Normalize [tex] \Psi [/tex] (that is, find A, in terms of a and b).

(b) where is the particle most likely to be found, at t =0?

(c) What is the probability of finding the particle to the left of a? Check your result in the limiting cases b=a and b = 2a

(d) what is the expectation value of x?