We have to find the points of (a) maximum and (b) minimum probability for a particle trapped in an infinitely deep well of length L if the particle is in the state n.

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The wave functions of a particle that is trapped in an infinitely deep well of length L are

Note that

The probability density is proportional to

(a)

Therefore, the points where the probability will be a maximum will be determined by the condition

(b)

The points where the probability will be a minimum will be determined by the condition