Homework 1

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

.

Problem 2:

The wave function of a particle at t=0 is 

.  

At t=0, what possible values of the momentum of the particle can be found, and with what probability?

Problem 3:

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 and of their travel.