[UPSC CSE 1991] Schrodinger’s Wave equation and applications (Q235, 60M)

Set up Schrodinger's equation for a free particle confined in a cubical box and find the energy eigenvalues. What form will Pauli principle take for electrons in such a box? Deduce the zero point energy if the length of the box be 10^{-10}\text{ metre} and there be 10 electrons in it. (The coulomb interaction maybe disregarded.)