(Solution) - A particle is confined within a box with perfectly rigid -(2025 Original AI-Free Solution)

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A particle is confined within a box with perfectly rigid walls at x = 0 and x = L. Although the magnitude of the instantaneous force exerted on the particle by the walls is infinite and the time over which it acts is zero, the impulse (that involves a product of force and time) is both finite and quantized. Show that the impulse exerted by the wall at x = 0 is (nh/L)i and that the impulse exerted by the wall at x = L is -(nh/L)i.