The short version. If you're curious about how the x matrix for a harmonic oscillator moves an element within the oscillator state column matrix, this post may hurry things along for you. I was curious and spent bits and pieces of a few days trying to work it all out. Here's what I found hastily jotted down so I won't forget and so I can get back to studying for finals.

We're rapidly plowing towards finals week, so this may be rather disjointed, but I wanted to capture a few notes on actually using matrix operations before they escaped. In Hecht's book when calculating the perturbtion of an harmonic oscillator due to an x ubed, or an x to the fourth potential he makes a rather light reference to using the 'known' matrix elements of the x operator of the harmonic oscillator. I've seen the references quite frequenlty and decide for once rather than just using the elelments the book wrote down, seeminly from nowhere, that I'd go calculate them. I…

We're rapidly plowing towards finals week, so this may be rather disjointed, but I wanted to capture a few notes on actually using matrix operations before they escaped. In Hecht's book when calculating the perturbtion of an harmonic oscillator due to an x ubed, or an x to the fourth potential he makes a rather light reference to using the 'known' matrix elements of the x operator of the harmonic oscillator. I've seen the references quite frequenlty and decide for once rather than just using the elelments the book wrote down, seeminly from nowhere, that I'd go calculate them. I…