A particle in a box of length is in the state
such that its wavefunction is
What is the probability that the particle is in right half of the box?
Solution
The probability density associated with the given wave function is
The probability that the particle is in right half of the box is the integration of this probability density from to
. Thus the required probability is
The result of this integration should be (Work out this integration).
Thus the probability that the particle is in right half of the box of length in the state given in the problem is
.