1.) Use a plotting program to plot the solutions to the harmonic oscillator Schrodinger equation, for v = 0 and v = 2. Calculate <x>, <x2>, <px> and <px^2>, and the product uncertainty of x & uncertainty of px for these two functions. Provide a physical explanation for the results.

Notes:

1. Use a QM textbook to identify the solutions to the harmonic oscillator equation. I recommend using a symbolic math program to solve these equations, but please set-up your integral by hand, first.

2. Note: Uncertainty of G = sqrt ( <G2> - <G>^2 )

Question 2.) Prove that the n = 1 (ground state) and n = 3 (second excited state) wavefunction for a 1-D particle in a box are orthogonal.