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 .