5. (a) For a particle placed in an infinite potential barrier of width a, for which V(r) = 0 for 0 < r < a, show that a2 Ar? = (r²) – (x)² %3D 12 %3D n272, (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 < a < 2L/3. From the general formula for arbitrary n, find the limiting values as n 00.

5. (a) For a particle placed in an infinite potential barrier of width a, for which V(r) = 0 for 0 < r < a, show that a2 Ar? = (r²) – (x)² %3D 12 %3D n272, (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 < a < 2L/3. From the general formula for arbitrary n, find the limiting values as n 00.