Problem 4 - Quantum Harmonic Oscillator Eigenfunctions The first two eigenfunc- tions of the quantum harmonic oscillator are (a) 1/4e-ax/2 40(x) = V (x) = (4) 1/4 -ax/2 xe " where a = mwo/. (a) Verify that these two functions are indeed eigenfunctions of the quantum harmonic oscillator Schrdinger equation. (b) Verify that these two eigenfunctions are orthonormal functions on -0 x +. (c) What is the eigenenergy of each eigenfunction? (d) Are 0 and eigenfunctions of the position () and momentum (p) operators? (e) What is the uncertainty Ax Ap in the simultaneous measurement of position and momentum in vo?