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7. Consider a particle with normalized wave function
S Nxe-/2 if 0<x<∞
V(x) :
elsewhere,
where a is a positive real constant and N = /a³/2.
(a) Write down an expression for the probability of finding the particle
between x and x+ dx. Illustrate how this probability depends on x
and find the most probable value of x.
(b) Find the expectation values for the position and the square of the
position, (x) and (x²).

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