I was trying to resist the temptation, but those are the magic words.
Well, not really, since I had already started working on it some. Here's where I attempted it a while back, if anyone cares to wade through the mess. I put most of my earlier calculations in ATM when I wasn't so much asking a question but wanted help and verification when working something out. One might start toward the end and work their way backwards or something. I had a couple of mistakes approximating in the beginning. In any case, I'll try to find a simpler method that I can post here for just the magnification.

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Let's put together the pieces of The Grand Puzzle . (website - now revised)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."