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) + mω2x2.

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.