**Problem 1:**

The ground state wavefunction for a particle in a one-dimensional box of length *L* is

Suppose the box is 10.0nm long. Calculate the probability that the particle is between x=4.95 nm and 5.05 nm.

**Solution:**

The probability of finding the particle between *x* and *x* + *dx* is given by
. Therefore the required probability is

**Problem 2:**

The ground state wave function of the hydrogen atom is given by

*a*_{0} = 0.53*A*^{0} is the Bohr radius. Calculate the probability that the electron would be found somewhere within a small sphere of radius 1pm centred at the nucleus.

**Solution:**

The required probability is

2007-09-27