(Simple Harmonic Oscillator) For a simple harmonic oscillator, the potential V(x) is given as V(x) = mw2x2. In this case, the unnormalized wavefunction is given as _n(x) = mw(1/2)H_n(z), where n = 0, 1, 2, ...
Here, H_n(z) = (-1)ⁿ e(z2/2) dn/dzn(e(-z2)), where z = (mw)(1/2)x.
(a) Find the energy eigenvalues by solving the time-independent Schrodinger equation explicitly. Show that the energy levels are quantized.
(b) Discuss qualitatively why the energy levels are quantized. You can use your result from
