Problem 1:

Use the uncertainty relation to find an estimate of the ground state energy of the harmonic oscillator.  The energy of the harmonic oscillator is E = p²/(2m) + ½mω²x².

Problem 2:

Electrons of kinetic energy 10 eV travel a distance of 2 km.  If the size of the initial wave packet is 10^-9 m, estimate the size at the end of their travel.