Quantum Oscillator Operator Approach Part 2

We finish constructing the "ladder" of states for the quantum harmonic oscillator using raising and lowering operators, and use this to solve for the eigenfunctions and their energies.

[@CalBruin]

Question: @4.45-4.57, how did you get sqrt (m w/s h-bar)? What am I missing the coefficient to the x in the exp comes down. Why are there not two terms still, given the (h-har d/dx + max) exp (-stuff x^2) ? In other words, here is my problem, I am reading the math as f1 = stuff * (const * D/Dx + 2nd term) f which should equal stuff * f' + 2nd term * f = stuff * f' + 2nd term * f turns out f' = (exp stuff) * f, so = stuff * (exp stuff) * f + 2nd term * f factor out f, = f (stuff * exp stuff + 2nd term)