A particle is confined between rigid walls separated by a distance L. We have to show that (a) the probability that it will be found within a distance from one wall is given by

We have to evaluate the probability for (b) , (c) , (d), and (e) under the assumption of classical physics.

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(a)

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

Note that

The probability density will be

We normalise by requiring that the probability of finding the particle any where between and has to be one. That is we have the condition

, or

The normalised probability density function in the state n is therefore

The probability of finding the particle within a distance from one wall will therefore be

(b)

The probability for will be

(c)

The probability for will be

(d)

The probability for will be

(e)

Under the assumption of classical physics, the probability of finding a particle that is trapped between rigid walls separated by a length L will be uniform, and therefore the probability of finding the particle within a distance from one wall will be

.