If a particle conned to move in one dimension has wavefunction ψ(x), then the probability of nding it between any two points x1 and x2 is: P(x1, x2) = ˆx2 x1 dx |ψ(x)| 2 Calculate the probability of nding a particle between x1 = 0 and x2 = a/3 for the ground-state of a one-dimensional rigid box of size a. [Hint: the calculation involves an integral of the function sin2 θ. Use the identity 2 sin2 θ = 1 − cos 2θ.]

Step-by-step explanation:

The probability of finding a particle between two points is given by:

Furthermore, the wave function of a nth state is given by:

By replacing we obtain

and by using the relation,

we get for the ground state (n=1):

hope this helps!!

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