(Solution) - For a particle in a one dimensional box of length l -(2025 Original AI-Free Solution)

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For a particle in a one-dimensional box of length l, consider an infinitesimal interval of length dl that lies within the box. For each of the following stationary states, state which location(s) of this interval gives a maximum probability and which gives a minimum probability to find the particle in the interval.
(a) n = 1;
(b) n = 2;
(c) n = 3.