- #1
vorcil
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At time = 0 a particle is represented by the wave function
[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?
[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?