**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 = p^{2}/(2m) + ½mω^{2}x^{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.