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

(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(a) = 0 for 0 <I < a, show that a2 6 Ar² = (r*) – (1)² = "(1-) 12 n2n2 (b) For a particle in a one-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 00.
Transcribed Image Text:5. (a) For a particle placed in an infinite potential barrier of width a, for which V(a) = 0 for 0 <I < a, show that a2 6 Ar² = (r*) – (1)² = "(1-) 12 n2n2 (b) For a particle in a one-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 00.
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