5. (a) For a particle placed in an infinite potential barrier of width a, for which V(r) = 0 for 0

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5. (a) For a particle placed in an infinite potential barrier of width a, for which V(r) = (0 for 0 <z < a, show
that
Ar² = (2²} – (x)° = (1- )
(b) For a particle in a onc-dimensional box, calculate the probability that the particle will be found in the
middle third of the box: L/3 <x < 2L/3. From the general formula for arbitrary n, find the limiting
values as n → .
Transcribed Image Text:5. (a) For a particle placed in an infinite potential barrier of width a, for which V(r) = (0 for 0 <z < a, show that Ar² = (2²} – (x)° = (1- ) (b) For a particle in a onc-dimensional box, calculate the probability that the particle will be found in the middle third of the box: L/3 <x < 2L/3. From the general formula for arbitrary n, find the limiting values as n → .
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